Big FE fan here so this got my attention!
The sprites are really nostalgic
The roguelike approach is interesting, but also clashes directly with FE basics IMHO. In particular, Weapon Triangle doesn't really matter if you don't actually get troops with different weapon types, like my most recent run had me with multiple sword wielders but zero axe/spear users. Following on that, the game kept "rewarding" me with axes and spears in that run which I couldn't equip. Or a resistance booster item when there were no magic enemies for multiple battles.
Then some runs I literally didn't get any starting troops at all. Was playing the web browser version for what it's worth.
I think the roguelite should be "rigged" so you always start with at least 1 sword, 1 spear and 1 axe unit minimum. There could still be plenty of randomness with the specific unit types you roll, but at least you'll always have somebody.
In alternative, take a page out of 3 Houses and allow any class to use any weapon type (or melee physical can use any melee physical weapon so there's still distinction between bow users and mages). Maybe units still get a bonus with their favored weapon, but that way at least if you find a cool weapon you can still use it regardless of which units you rolled. One of the most fun aspects of roguelikes is how you can find a completely different weapon that changes your playstyle mid-run-
Also as others pointed out, the UI could be a bit more intuitive.
Still pretty great work all around, was fun thanks!