At this point it's hard not to feel badly for Aira. She's had even less say in her life's new trajectory than Sei, having been summoned and summarily whisked away to live out the isekai dream…only to almost certainly begun to hear rumors about not actually being the Saint. From what we've seen of Prince Kyle, including in this episode, it's not hard to think that he may not be all that receptive to listening to any concerns she might have about whether or not she's really the Saint, which puts her in an untenable position: she's been ripped out of her world and now she's got more than an inkling (according to her facial expression at the end there) that she's not actually the person they were looking for…and the person who most needs to understand that isn't interested in listening.
It's also an interesting statement on the isekai habit of having teenagers be the Chosen Ones. Yes, that's a very common facet of young adult literature the world over, but it's also taking people who don't necessarily know how to exercise their agency and thrusting them into a role that they may not be all that keen on. How Sei is handling things versus how Aira is makes for a good example. Sei knows she is the Saint, or has at least figured it out over the months she's been in Salutania, and is able to pick and choose what that will mean for her. She's able to make things feel emotionally comfortable for herself while still preparing to be “discovered” and thinking about what that's going to mean for her. She's made friends and forged relationships that can help her and sustain her going forward. Aira, on the other hand, hasn't been able to do anything but go along with the plan that Kyle has laid out for her. She's not stupid and has clearly been hearing the rumors about Sei, but she's also not comfortable forcing herself to be heard and in a position where she's been made to play a role she knows doesn't entirely fit. Where Sei is able to create a new life for herself, Aira isn't confident or mature enough to do the same, and that's led to her being lumped in with Prince Kyle. To say that it could have disastrous consequences doesn't feel like overstating the matter.
Those consequences really could be coming sooner than Kyle thinks now that his father the king has all but verbally acknowledged Sei as the Saint. (Bowing his head to her in full court seems like a pretty concrete admission of the fact.) Sei knows it too, and that's not making her all that comfortable. She really doesn't want to give up her life at the Research Institute, nor does she want the notoriety of being the Saint, although it seems clear that she's going to have make some concessions on at least one, if not both, of those fronts. Requesting magic lessons is a good way to help the king save face – not claiming a reward would have made her look not so much Saintly as it would have indicated that she didn't forgive him for Salutania's treatment of her when she first arrived – and if the courtiers think that she's being too modest in simply asking for schooling and access to the restricted collection at the library, they seem willing enough to write it off as her being humble. But mostly Sei's buying herself some time to keep thinking about how she's going to handle things. She knows she can rely on Johan and Albert, but she still needs time to get used to the potentially huge change in her life, the second in less than a year. She's also really not keen on being sent into battle as the Saint, and I can't say I blame her – but it's also understandable that as the grown-up in the situation, she doesn't want to make Aira do it in her stead.
Speaking to the adaptation for a moment, I'm really pleased with how neatly this is skirting around having to use the RPG status screens that are present in the novels, both because I find those intensely annoying and because it proves that they really aren't necessary. Sei doesn't need a number to quantify her magic power; all we need to know is that she has more than Yuri for the plot point to work. I also find it interesting that where the books specifically mention corsets and gowns more similar to European fashions of the 18th century (and Johan's outfits bear that out in the anime), Sei's court dress is much more Medieval by way of the 1970s with that turtleneck. It's neither here nor there in terms of quality, but it certainly looks more comfortable – and comfort may be increasingly important as Sei's forced to publicly acknowledge that she is, in fact, the Saint.