I think you're onto something really great with this concept and with a little more polish and balancing you have a real gem of a game.
The main gimmick while neat in theory is a bit obtuse with how it works exactly. I had to restart pretty early in a run because I accidentally removed all my offensive / damaging abilities. A default, always-there attack would do wonders to fix that issue.
The movement works really well for the type of game you've made, though I would have liked a bit more feedback on enemies when they got hit by a bullet. I wasn't sure if the bullet did hit them or if I missed.
I also think that the enemies are a bit "bullet-sponge-y" in general and would probably benefit from having their health reduced a tad.
While this might sound very nit-picky and negative, I really do believe that if you manage to fix and tweak some stuff and add a bit of game juice, this game would be really good! The foundation is there and it is solid!
Amazing work!