It's impressive that someone so much younger could get in here, and besides she carried with her a kind of reputation with how well she'd managed at the exam and how hard she worked. Higata can't help but be impressed by her.
Ryuu's something else too, though, to become an apprentice at the age of ten and training an apprentice at the age of twelve. That's amazing!
Higata knows that it takes a lot of work and a whole lot of study, applying what one studies too, to end up as a Court Herbalist Apprentice, and a lot of work and study and apprenticing before one ends up as an official Court Herbalist.
So, he's really impressed by Shirayuki. She's worked hard to get here too, he knows, and he admires her. She must have been spending her whole life studying herbology to do well on the exam, especially her first time taking one, and to get in.
He's worked hard most of his life, spent countless hours studying, watching plants, taking care of them, making herbs, and being an apprentice to more seasoned herbalists, before Higata could end up here and able to pass such a notorious and difficult exam.
There were only two who passed the last time anyway, and one was Higata, and the other one was Shirayuki. So, he knows that it takes years of hard work, and therefore, Shirayuki is more than qualified and he's a little awed in a way.
Like she's so skilled at a younger age! She had to have worked impressively hard to get here, and so, Higata is aware that this isn't an easy task. Their work isn't easy, at least not at first anyway, and it takes various people to train someone.
And Higata trusts Shirayuki as an herbalist to another, because to get in here takes serious skill, serious dedication, serious work, and probably more than a few late nights studying, and probably more than a few late nights, watching home grown plants to see just what differences the night and day have on them by personal experience and not merely intellectual knowledge.
So, Higata knows Shirayuki's a capable herbalist, and he's happy to be hired on and trained at the same time as someone else who knows her stuff.
And the fact that she's younger than him, another young hiree, like Ryuu, though older when hired than he was, and well worth every ounce of admiration he has, definitely.