(Vague spoilers from up to chapter 700) This is going to be super long, but it isn't really negative and should all be constructive, so buckle up lol.
First and foremost, I love some of the fluff bits. I'd even go as far as to say it's one of this novel's strong points. But like you said, there are times where it just feels like nothing is moving forwards, and I think I know why.
I think a part of the problem is the pacing. One of the reasons for that is that sometimes, this isn't really treated as only Kat's story. Rather this is Kat, Jahi, Anput and Leone's collective story. Switching to their perspective so often and needing to cover how they progress slows things down a bit because it's almost like you're writing 1 3/4's of a story. There are times when we have several chapters back to back that all take place in the same day just from everyone's pov.
Now don't get me wrong, I don't think that's a problem. That's just an objective observation. In fact I'm glad you do it so it doesn't feel like they are just side characters instead of true romantic love interests. Their relationship wouldn't work as well as it does without the insight into them individually. That said, it does slow things down, especially when this story often goes at a pace of only a few days passing at a time. Sometimes even day to day.
Basically, I just think there needs to be larger time skips every so often. These girls are supposed to live for hundreds if not thousands of years, so it's kind of wild that not a single one of them is even in the double digits yet. If I'm not mistaken it's only been like, what, three, maybe four months or so since Kat returned from her involuntary sight seeing trip? And yet that was almost 300 chapters ago soon. She left around 270 or so. Spent a few months, at most, away and returned 420. So about 150 chapters to cover a few months. Not too bad, until you consider several years passed before that event until they got to school. And that everything after that all takes place during the same year. I'm not sure an entire year has passed since they got to school and certainly not since they passed their tests. Going by logic at least, a year should have passed, but it doesn't really feel like it. It actually feels like more should have passed by, but the characters make it seem like less actually has.
And that leads to my final point. I think you're both making them grow too fast while also trying to prevent them from doing that exact same thing. They're only 8 (at least Leone was confirmed to still be 8) and have only been training for, what, 3 to 4 years now? If I'm not completely remembering things wrong, Kat "woke up" when she was 5, right? So how come after only 3 years are they even remotely close to a knight's level? It just kind of undermines the power level of the entire world, ya know? I get they're all very special in their own ways. Once in a lifetime talents. But 3 years of training, even from the best teachers, really shouldn't have them where they are now. I just feel like that was from a combination of not wanting them to grow too quickly through huge passages of time, but also needing them to be that strong to even progress in the first place. So you're stuck in a place where they are making a lot of progress but no time is actually passing. A bit of a conundrum if you will.
Now, I don't have too much in the way of solutions this far into the story but I would recommend just biting the bullet and giving the other characters levels or at least level approximations. Effective levels if you will. This is only because, as it is currently, it's really hard to judge how strong anyone is in this story. We know the peek with the empress, but we don't really know how far away that peek actually is. Kat is making progress but when you don't really have anything to visually compare that with, it feels like it might as well not even matter. When you have her effectively on a similar level to Jahi, then have Jahi constantly sparring with her mother, it just feels like they're already near the top. Even if logically we know how much her mother has to be holding back, without any actual indication, it's hard to place. In fact, due to Chodeva essentially being treated as a plaything by Lady Fenryas just like everyone else, it just makes it feel like they're around the same level. I would recommend giving her someone serious to fight that the girls can't help with to truly show the gap between them and more importantly, how far they all still have to grow. There's a reason most action novels have some kind of ranking system. Cultivation, adventurer ranks, knight ranks, mage tiers, levels, etc.
In any case this ran a lot longer than I thought but I hope it helps.