So the armor storm fighting style at lv 1 you can treat your unarmed attacks when wearing heavy or powered armor as if you were wearing a battle glove of your level or lower.
When I go to the equipment guide I only see 4 battle gloves listed, lv 1, lv 10, lv 13 and lv 17. Does this mean you only get damage upgrades at those levels? Are you stuck doing 1d4 till you are lv 10?
That's all the battle gloves listed in the CRB. I guess until we get something like "Ultimate Equipment" or some more content, you are correct.
If this is for a home game, you could always ask the GM to make stats for a level 5 or 6 battle glove, and use that for the weird gap.
You do get Weapon specialization and the str x 1.5 damage additions in there.
Most weapons don't really get a lot better until around 7-9 anyway. For example:
spear is 1 die at level 1
2 dice at level 7
3 dice at level 10
7 dice at level 15
12 dice at level 19
Thereby gaining 2 dice over the first 10 levels, and 10 dice over the next 10 levels.
Battleglove is slightly behind, but it also doesn't need to be drawn (generally) and gets 1.5x strength from armor storm. Seems pretty balanced to me as a backup attack.
Slightly different question: Can you put weapon fusions on the Armor Storm Hammer Fist feature?
I am leaning toward not, since its not actually a battle glove. Its just kinda annoying that if something has DR magic, your fist is the only weapon in the game that can't bypass it. Can you even use Rune of the Eldritch Knight on it from taking Arcane Assailant as a secondary style? Since its not actually a weapon?
Hammer Fist uses unarmed strikes which has no item level (not even zero) so no fusions for Hammer Fist. You'll get to the point where you're better off going with advanced melee weapons (go pulse gauntlet if you wanna keep the "unarmed" aesthetic) as you'd just be missing out on the +2 damage bonus from already having Melee Striker gear boost + Hammer Fist, but you can benefit from usually better number of dice and fusions which would be stronger than Hammer Fist's +2 damage bonus.