The game is wildly different from any Fire Emblem thus far, but there's alot that makes me think they were very conscious about learning their lessons from Fates, which is very good! The lore and writing are vastly improved, and the supports also incorporate something I've been wanting, which is that not everyone can A support. It's a much more natural exploration of the characters than assuming anyone can marry anyone, I hated that. That's one of those things that Fates took and continued from Awakening, that marriage simulator aspect.
Fates continued on the popular parts of Awakening (marriage simulator, baby optimizing) while strengthening the weaker parts (fixing the broken gameplay and poor ai/map design). 3 Houses on the other hand seems to have ignored both in favor of what modern Fire Emblem has become, by really, and I mean really, expanding on the social/customizing aspect of the game. I don't know that the customizing system is more indepth (or intuitive) than Fates and Awakening's, but it feels nicer. I didn't like having to remember what classes each character could reclass into and what skills I was trying to pick up, and having that all in one location for all the characters is so much easier for me to manage. Also it reinforces the social aspect of the game, since it feels like you, the player, through the avatar, are guiding the characters along their education.
If Fates was an evolution of Awakening, then 3 Houses feels like an evolution of SoV. Which would make sense, both Fates and 3 Houses use the same base engine of their predecessors. But not just how the engine feels, but how they manage themselves too. The actual battling portion of 3 Houses' gameplay is really... not there. It's just sort of a playground to see how your units are progressing skill and ability-wise. The real focus of the game is in the storytelling, kind of like SoV was, though unlike SoV alot of what you do outside affects how well you perform in the battles, so it's less a flaw and more of a design choice to focus on other things I guess. It's alright, and maybe it "gets better", but I also completely understand if it doesn't. I cannot imagine, nor would I want to, having Conquest-style maps in this game. Although, there are some small things from Fates I do miss like how fluid the controls felt or the pair-ups (even if only to make transporting units easier. Kind of surprised they took this mechanic out, honestly, although there's that attendant? mechanic I haven't tried yet). The one thing that fills me with dread about this game is it's so darn long! I know there's a timeskip and I feel like I'm not even a quarter of the way through the pre-timeskip. Thank god I chose normal difficulty, that was a correct decision. I don't know if I'd call the pacing slow like you did (even if it does take its good old time), but I can easily see myself sitting here 80 hours later and not even finishing my first playthrough out of three. This would be less of an issue for me (I actually didn't super mind SoV's gameplay), but it's daunting when I'm limited on time now out of school.
One final thing I'd like to say, and there are tons of tiny comment's both good and bad I'd like to make, but the one I felt like needing to say, was how unconvincing Byleth's competency is in the opening of the game. The only thing he does is almost get killed trying to save Edelgard (who probably could easily have defended herself if the cutscene didn't confiscate her axe for some reason). Like isn't he supposed to be a mercenary his whole life, really strong? The first thing we see him do is almost die from something silly. Sure, time-shenanigans means that what the students saw was him fending off the bandit, but it doesn't convince me, the audience, that he's at all as impressive as everyone seems to be. That was a big disconnect the first couple of hours.