Alright so here goes the braindump proposal for the Covenant in 40K…
The assumptions:
Tide finds a way to "individualize" his creations so that he doesn't need to puppet them 24/7. Assuming this is a feasible end goal as his stated intent is to create life and puppeting forever sounds like a hack to fulfil this goal.
Covenant lifeforms are not 100% pure flood genetics, but whatever genome Tide engineers up for them. They however do retain Flood cells within them (will elaborate on this later), similar to the Altered. As a result they have some ability to communicate with Tide as individuals.
Members of the Covenant are somewhat aware of who Tide is. They recognize him as their creator but one that doesn't wish to be viewed as a god, and thus act accordingly.
I assume you'd want the Covenant species to feel somewhat recognizable, so you're not going to want radical changes where the Prophets end up looking and acting like the catgirls from Nekopara… right?
Society/Culture
Covenant lifeforms are going to have their own individuality but awareness of Tide the Flood. He's not going to be worshiped per se due to him not wanting as such, at least by the majority, but naturally he's going to be respected in some sense as a greater being or even a parent. Thus the Covenant here practice less of an dogmatic religion and more of a shared community spirituality. E.g. a sort of Zen-like philosophy view of life as Tide already somewhat does, with the view that all life and their souls are capable of being connected, the Flood as the embodiment of this ocean of life, Tide as its curator/guardian, and The Domain as the afterlife.
Given that Tide is in every member of their society, it might also be possible for individuals of the Covenant to psychically connect with each other through the Flood, aiding in cross-species communication/translation. Maybe incorporate/reinforce this through meditation rituals that Tide was making his puppets do near the beginning of this fic? It shouldn't be something that is easy to do all the time, should be only doable through effort. This does however have a calming effect as a whole on the society, with conflict having easier ways of being resolved and just overall more unity, not necessarily agreement but understanding, given that direct mind-to-mind communication is possible. Having Tide cast judgement on a conflict would be like having the Supreme court issue a ruling. Being a semi-hivemind society with a central intelligence present, I think Tide will be their distant symbolic head of state, similar to how Canada/Australia treats the Queen/King of the UK as theirs. The actual government will be a council like the Covenant is in canon, only more technocratic/meritocratic in nature, with no single supreme leader and decision making done by consensus.
The Covenant, like the Tau, are going to tend towards a caste-like society due to how Tide can and should optimize species genetics to be specialized at a particular set of things. However, one thing I think would be interesting is if Covenant lifeforms had the option of being able to change their species depending on preference and demonstrated ability. It would probably involve a rather elaborate ritual ending in culminating in residing for a whiles inside an incubator that looks suspiciously like a Carrier form, and be reserved for only truly needed cases.
Given the circumstances of the galaxy they are in, most Covenant will probably be educated on the specifics of what Chaos are and how they influence/manipulate beings. Their main societal goal will be aligned with Tide - bringing balance to the galaxy, the elimination of the corrupting forces of the chaos gods and other players in the great game. That is the Path of their Great Journey in this universe, this is what they were literally created to do.
Now let's get into the individual species:
Lekgolo
Much of Covenant society revolves around the Lekgolo. The Lekgolo are the closest to pure Flood, just locked to a particular set of forms (none of which look like a rotting corpse please), and contribute their biomass directly to the Flood, unlike the other species who are distinct genomes. They can become many different forms, each one able to fuse/split/metamorphosize into different things, but their primary forms are that of the typical worm as in canon. Flood-like spores can be one of the Lekgolo's methods of propagation and act as a symbiotic organism inside every single one of the Covenant, just like the Altered. The carrier form is made of many of the worms fused together and serves as an incubator of sorts for the sick or those undergoing biomodification, which this Covenant uses extensively. So to the outside observer, the Lekgolo are the Flood, with autopsies of Covenant showing Lekgolo cells within them it should be the obvious conclusion.
Similar to how canon Covenant uses them in certain applications, the Lekgolo are treated as a form of biotechnology but more widespread in this 40K universe. I think you already touched on this idea a previous post, the Covenant being a civilization that leverages bioforms extensively would be one way for them to stand apart from the Tau. Lekgolo are present as components of vehicles like they are in canon (e.g. in the Scarab), used as terraforming seeds (worms can create biomes), used as synth muscle replacements in power armor, and even used in construction secreting substrate to create massive infrastructure (maybe top it off with them being used en masse to create a Halo Array which serves as a mobile capital worldship similar to how High Charity is used).
Similar to canon, Mgalekgolo Hunters fulfil a role in the Covenant army as an equivalent of a Dreadnought, a walking bio-tank… just without the weird backside weakness please. The Engineers, the Huragok can just be an amalgamation of Lekgolo in a form used for maintenance and construction projects, which isn't really too far of a stretch given how both have a relationship with Forerunner constructs in canon. The Covenant use Lekgolo Pods (which are in the shape of an infector pod but look much "nicer" in being just several Lekgolo fuzed together) as an emergency healing aid, using its own biomass to heal and stabilize wounds. If you're scared of AI getting corrupted by chaos, having all Covenant computers be just specialized Lekgolo constructs (really Dune-esque) is one way to get around the issue. Last rites of the Covenant involve offering the body of the deceased being into a Boil (taking terminology from Sid Meier's Alpha Centauri) of Lekgolo, symbolizing returning the deceased to the Flood that connects life, and also conveniently recycling the biomass.
Kig-Yar
Jackals. In this version, they are the most populous of all Covenant species instead of Grunts. A jack of all trades species, being present in some form in basically every level of Covenant society. Not as strong as humans in certain ways, but more than makes up for it by being extremely agile. Anyone who has played legendary knows these guys are extremely accurate shots to the point of aimbotting, keep it like that. Now imagine facing hundreds of them with lasguns. They don't like to participate in melee, just constant kiting of enemies to exploit their agility. Other than just toning down their bloodthirstiness (the Kroot already exist for that), no need to modify them too much from their canon depictions, keep them the pragmatic and mercantile sort. Although I'd probably say that their energy shield gauntlets are better given to species who actually do well in melee like the Brutes and Elites, those things are actually kind of overpowered. Non-game media does state that a lot of other species use them when given a chance (like even Spartans jury rig them).
Yanme'e
The drones. They differ from their canon counterpart in that here, they're not individually sentient and that they don't need gravity modules to assist with their flight. They are all part of a hivemind psychically controlled to by their queen who occupies a generally high authority in the Covenant like they do in canon. Think of incorporating genomes from that wasp hivemind that Tide found below Malum in the first few chapters. Since they're not individually sentient, they are often used as an expendable labor force in the Covenant for riskier jobs. They are much more numerous here than depicted in the Halo game, used as forward scouts and unit level air power. If the covenant military needs to cover a retreat, the opponent is going to suddenly get swarmed by these guys. The Queen can modify the drones she gives birth to, making specialized variants, kind of like how certain irl eusocial insects are able to specialize their own species. Taking an idea previously made in this thread, one of the most notorious combat variants is the Sentinel, a drone with a Lasgun / concussion rifle / Volkite ray weapon integrated directly into its head. It is smaller than the regular drone since it doesn't need many manipulators to do heavy labor work, and protected by a metallic carapace. It is fast and capable of being mass produced in swarms, so extremely annoying to fight. Go ham with other variants if you wish, plenty of alien insects from other scifi series to take inspiration from, and before long you'll have the guardsmen chanting E.D.F. instead of prayers for the emperor.
Jiralhanae
The Brutes. A misnomer of sorts. Brutes differ from their canon counterpart by not being overly aggressive son of bitches but rather just plain simple folk. A Brute is not going to spin lies, he's going be brutally honest with you. They are a whole subculture in the Covenant of just getting straight to the point without any bullshit, and serve a sort of foil to prevent the Covenant from becoming a do-nothing navel gazing society like what the Jedi turned into in Star Wars. They're not stupid or hotheaded, they're just blunt and direct, which does cause them to rub heads with other Covenant, but not in an overly negative way like they do in Halo canon. Physically they have the strength of and size of Orks, so they're going to fulfil some role of heavy muscle in Covenant society. Within the military, what better way to use that than shock troops for close combat fighting? The Brutes are renown for leading melee charges and almost exclusively carry heavy weaponry. Plasma turret cannons, fuel rod cannons, grenade launchers, oversized shotguns and especially the 40K bolter fit Brutes well. Give them the Jackal's shield if possible, or if not just the standard 40K metal shield similar to what ogryns use. Chainswords and of course the signature gravity hammer for their Cheiftans.
Sangheili
The Elites. They fit their name. In the Covenant, the Elites are renown for being dedicated to their craft. In any sort of job or role, the Elites strive to be the best as per their name. Within the military, they are the bulk of the special forces, occupying a role somewhere in between Tempestus Scions and the Astartes. I think people here already know what Elites do, so just keep them the same. They should be the Covenant species with the least alterations to physiology and culture, other than just adjusting their faith. There better be energy swords and there better be a champion role called the Arbiter. Also if you want Titans to rival the Emperor Titans, make it take the shape of a large purple elite and call it an Evangelion lmao.
Unggoy
Here's the biggest divergence. The Unggoy are not typical Grunts here. They are instead almost never seen on the battlefield. Their body plan has significant modifications. They are a bit larger than they are in canon but not too much. The big difference is that Unggoy have two brains. A small individual brain in their head and a second much larger brain they carry in a hump on their back. In Halo canon, they wear armor with a backpack and they look really weird if you take it off. I've always thought back since the first Halo CE that their backpack was actually a part of their body so that's where I get the idea from for this. This brain hump they have can be shared as a mini-Keymind for the Flood. As such, the Unggoy have natural telepathy but NOT psyker ability. Their gigantic brains allow them to serve as a sort of thinker caste within the Covenant, having outsized representation in professional roles like scientists, engineers, teachers and high level leadership. A strange reversal of the grunt role they take in canon. If you want to keep the Grunt name, just say that due to their natural telepathy they have reduced ability to verbalize, only speaking in grunts.
San'Shyuum
I dunno about them, but the Prophets can be an innate psyker species that Tide can create much later on. It does fit the whole "prophet" name. Obviously a very rare species to nerf them being all innate psykers. Not really much to say here, just make them less ugly and not the politicking assholes they are in Halo canon. Due to their numbers you're not going to see them much in the leadership, though with psyker abilities you still might find a few.
Humans
Tide started on a human world, having a tiny handful of humans in the Covenant is something that might just occur. But there's one particular subgroup of humans which would be beneficial - the Blanks. They're already hated by the rest of humanity, why not sneakily immigrate a few of them over to the Covenant? Presumably the Covenant can be made or conditioned to tolerate whatever anti-soul effect that Blanks emit. Then you can train them to be centerpieces of dedicated anti-Warp teams which you can call the Reclaimer Corps for extra spice.