Really neat as a proof of concept. The visuals and sound design is top notch.
The movement feels good but definitely has some issues with collision. It's kind of like being connected to a high ping server.
I think you should remove the player self damage so that you can do sick rocket jumps or shoot behind yourself to get a boost. With your movement system it could be a lot of fun.
Talking to the friendly tank while moving repeats your last input which made me drive up a wall the first time and off the map the second time. The projectiles seem to have some homing logic that occasionally makes them spin in the air. Also, I'm pretty sure you move too fast with diagonal inputs.
Overall the core mechanics are on the right track.