Context:
This takes place After LOTV ends but before the Epilogue, Raynor and Kerrigan are still around. The entire relevant Kopluru sector is teleported to the fringe of the 40k Galaxy in segmentum obscurus north of the eye of terror, but still quite for away from it. It is relatively isolated from the Imperium at first. (They are on the other side of the galaxy from the Tau so sorry, no interaction).
They arrive in M41 991
After the initial panic, several near-apocolypes happen relating to daemonic incursions and warp rifts due to the warp being so powerful in the 40k Universe. Millions of Terrans die and the protoss suffer, but they survive relatively unscathed. The thing is, starcraft already dealt with proto-daemons in Legacy of the Void with Amon, void/warp corruption, infohazards, etc, so they learned quickly. This would continue for months, but generally get under control "the psychic apocalypse" that will be discussed in the story
However, the Kopluru races capture a lost mechanicus scout ship, two months after the shift, and they get the WHOLE enchilada about the Imperium, and they believe all of it.
The Kopluru races form the Kopluru protectorate, a military alliance of mutual defense given the horrors they learned about and the sheer size of the Imperium.
(Starcraft takes place in a sector, 40k takes place in a GALAXY, they are outnumbered 1:1000000)
They follow the policy of constructive escalation, meaning that they are allowed to freely develop every single superweapon and technology that will give them a slightly larger chance of not dying. This also virtually eliminates any form of internal conflict as one betrayal would mean that all three of them die.
Psykers/the Warp.
The Void in starcraft is their Universe's Warp, they are the same. It operates along the exact same rules as the warp. Psychically sensitive people draw energy from the warp/void. But starcraft's universe is still in it's early stages, there hasn't been enough sentient life to generate enough emotions to create the Chaos Gods, so the warp is relatively peaceful, similar to before the war in heaven. Amon and the Xel'naga were advanced enough to ascend themselves to warp entities similar to the Old ones. Amon in Starcraft 2 acts as a proto-daemon/warp entity.
So psionics in starcraft will have a catastrophic awakening when they arrive in 40k with it's tumultuous warp. Millions will perish to warp incursions as the paltry defenses against psionic energy in the starcraft universe are overwhelmed.
Headcannon: The Xel'naga knew the potential dangers of the warp, so they essentially gave the starcraft universes technology to let them play on easy mode, and in 40k, these technologies will be the only thing stopping them from being annihilated instantly.
Non-warp FTL:
Starcraft FTL is non-warp FTL that utilizes a special artificial element found in vespene gas that shouldn't have formed under normal universal constants, seeded by the Xel'naga to allow the races to propagate faster and avoid warp travel. To create this element requires insane levels of technology, but to use this technology is very simple to use. Just ionize it with lots of energy, from a fusion reactor, for example, and it generates FTL effects. In starcraft, warp technology was discovered by the Terrans in 2300, very near future. A starcraft short story even says
"That the Terrans achieved warp travel technology speaks more to how EASILY KNOWABLE this universe is as opposed to any signs of native intelligence"
In short, it is reliable, and amazing over short distances, but worse over long distances. Starcraft FTL allows battlecruisers to conduct in-system tactical jumps, jumping in and out of planetary atmospheres, jump to only a few hundred feet above the surface of a planet, and operate in high gravity wells.
But it is slower across long distances. It took years for the UED to travel the 60K lightyears from earth to the Kopluru sector, and travelling across the Kopluru sector takes weeks. This is opposed to warp travel, despite it's dangers, being able to traverse 10,000 lightyears in 1-40 days (Imperial guard Codex), much faster.
It's basically a better version of pre-warp Tau FTL.
More refined usage of the element can lead to faster FTL travel in protoss tech, but will always fall short of actual Warp travel.
The problem is that this element that the Xel'naga created doesn't occur in the 40k Universe. It can still exist, but it dosen't occur naturally. It requires an insane, Necron-level of technology to actually make it, requiring pocket universes with altered constants to make it.
This is NOT fuel for FTL drives, just a component of the Drive, so they won't "run out" of it, but it puts a hard limit on the eventual number of FTL ships they can make, and larger ships require more of the material.
Obviously, this FTL material will become a priceless commodity that will be leveraged.
The Protoss, Terran, and Zerg use this.
FTL communications
use this same material as the FTL drives in tiny quantities, and operate on the same principle, shooting information into hyperspace. Great over short ranges (In wings of liberty, Raynor has a live conversation with Tosh over 6 lightyears) but after a certain distance, the signal slows, and then just dies and cannot be send further, again, astropathic communications are superior over long distances.
Psi-Matrix/warp network:
Protoss Khaydarin Crystals are WARP ENERGY FILTERS. Again, given to the protoss by the Xel'naga as train-wheels for warp-energy usage. The Central psi-matrix on Aiur, major protoss colonies, and motherships, are large networks of khaydarin crystals, are portals to the warp, and they can FILTER warp energy into "clean" energy. They create a reservoir of "clean" warp energy in the warp.
Then pylons can draw on this reservoir generated by the central psi-matrices through the warp from great distances to power structures. The range at which pylons can draw power from the central psi-matrix is the range of the "psi-matrix" (Pylons aren't power sources, they're just conduits to the central psi-matrix.)
The psi-matrix on Aiur can power things thousands of lightyears away, while a mobile psi-matricies aboard motherships can power things locally, in the solar system or on one planet.
Most importantly, since the protoss are good at mass-to information conversion, they can use this energy pool as a second form of FTL travel. Fleets, troops, structures, within the range of a psi-matrix can be transported extremely quickly, across long distances, or deploy quickly from orbit to the surface of a planet. Troops are sent into the psi-matrix on Aiur and appear through gateways on the battlefield.
This is limited by the range of the psi-matrix can exert.
This tech is not inflexible, so modifications can be made, motherships can teleport things to it from extreme distances beyond it's normal range during a mass-recall at great energy costs, psi-matrixes can be supercharged to directly deploy troops to the planet without needing local pylon power, (but it's too taxing to be used conventionally).
Warp gates are just able to tap into this energy reservoir more affectively.
Now in 40k, this filtration system is HEAVILY strained. Before, it would be like filtering lake water, now, in 40k, with a much more "populated" warp, it's going to be like filtering Raw sewage.
Khaydarin crystals and the psi-matrix will be under heavy assault from warp entities, so usage for it has to be reduced, and be more cautious, or else you'll have a daemonic incursion explode out of a Pylon.
Fortunately, in starcraft 2 LOTV, the protoss are familiar with off-grid alternatives due to, well, the majority of their race being mind-controlled and losing access to the psi-matrix. This is especially true with the purifiers, mechanical protoss, and the introduction of "solar reactors", artificial stars, (which are just glorified fusion reactors) as back-up sources of energy.
Most protoss ships have the conventional non-FTL warp drives for their own travel in modern starcraft.
Terran Defections:
The reasons there aren't many defections and simple.
Seriously, in starcraft's history, 2499-to 2506, there were three different governments and two major civil wars, each fighting for freedom. The Terrans were undesirables shot into space by the UED that made their own civilization. They're freedom-loving libertarians. They are completely opposite to that of the Imperium. Even people like Mengsk were more egoists and narcissists that didn't submit to the UED when they came around, obsessed with their personal power rather than the greater good of humanity.
The second more important thing is that the Terrans LOVE rampant technological development. Even the most authoritarian-minded Terrans, Mengsk, Carolina Davis, loved developing new technology, reverse-engineering xenos tech. This is something so inherent to Terran culture that it is immutable. The restrictions of the Adeptus mechanicus would have every single Terran regardless of political views up in arms in a heartbeat.
Production Capacity.
NO. BATTLECRUISERS AREN'T PRODUCED IN A MINUTE LIKE IN GAME
MARINES DON'T TAKE 20 SECONDS TO TRAIN.
But the gameplay reflects certain aspects of the lore, and that is insane production capacity. Again, Timescales. Starcraft Operates on different Timescales. There was only a 4 year gap between starcraft 1 and 2. In that time, the Terrans re-worked their entire arsenal, brought their fleet from a few battered Battlecruisers to being able to field 50 in an offensive fleet, many of which were new classes developed from scratch in those four years. You're seeing battlecruisers, the minotaur class at 900 meters long, being built in under two months from scratch.
While smash-and-grab raids, have direct-deployed troops, no on-site training/building, longer military campaigns and invasions can have Terrans set up their titular barracks, starports and factories and build a siege tank, Viking, etc in a few days or a week from local resources.
Backwater colony barracks and can build marine armor and ammunition on site-with local resources.
The Zerg and protoss are even more adaptable. This is all compared to 40k Timescales of decades and centuries. It takes a year for a hive fleet to get to the next system over. The starcraft races are all as adaptable and flexible as the Tyranids or Tau. This is not to mention that the Protoss now have a self-replicating war machine in the purifiers (robotic protoss) that are pumping out capital ships like no tomorrow.
