Honestly? You don’t even really need new weapon types. Could they be nice? Certainly. However, I am of the opinion that, in order for new, additional weapon types to truly matter, you would need to alter the core systems of Fire Emblem to make them feel like they aren’t just yet another option of similar “beatstickyness” for attackers to use. The existing weapon types that we already have should have more degrees of uniqueness brought to them (especially in the face of the weapon triangle mattering less and less) as it is, and I would much rather have that effort devoted to them than to making an entirely new weapon type before that.
However, I think one very unexplored aspect of typical Fire Emblem experiences is that most project leads don’t “shake up” the formula enough when it comes to the identities of classes, let alone what they promote into. Most projects will introduce branched promotions for every class or will add new classes wholesale to what the vanilla experience offers (including very interesting and, sometimes outlandish, ones - cursed swords, Rune-users, monsters, etc.), but, at their core, you still get Axe Cavaliers which promote to Great Knights/Paladins, Mercenaries which promote to Heroes, etc.
Even within the typical scope of sticking to the core FE class progression system, there is plenty of variance that could be undertaken to provide a fresh experience: Cavalry who have high strength stats and high movement, but are otherwise slow to attack, Myrmidons/Swordmasters who, as masters of the blade, have supreme skill and defense with them, Sages who are astute in all types of magic but not masters of any, Bishops who, with the authority of the church, are wielders of immense magical power and act as judge and jury with their rule, pirates who are able to weather the elements (Def/Res) because of their time at sea, Gladiators/Heroes who strike with quick reflexes, and so on.
Traditionally, one would not expect a Hero to have a 30 Speed cap or a Swordmaster to have a 28 Def cap. Maybe you change up weapons and make all Pegasus Knights use magic or bows instead of lances before gaining that tool as a Falcoknight. There are lots of things that can be done, even while sticking to a traditional “classline” as Fire Emblem is known for. But, this could also be expanded to truly shake conventions and foundations while still falling within FE’s traditional scope.
For example, Archers becoming Bow/(Sword or Dagger) Assassins. Fighters becoming Axe/Anima “Mountain Druids”, Pirates gaining Wyvern mounts to become Sky Pirates, Monks becoming walls of armor, using Light Magic and Spears as divine retribution… Even just within the animation sets that the community has crafted, there are endless possibilities for new territories of expansion to delve into, and, honestly, I think it would be nice to see that creep into more and more projects over time.
Maybe it’s because I’ve been a fan for close to 2 decades now and the “novelty” of more of the same has worn off on me, but it’s hard to get excited about something when I’ve seen it all before. When I was new to the series, sure, just feed me more of what wowed me and thrilled me, but I’ve come to find that I need new, fresh experiences and approaches to things to really get excited about what’s being offered.