Conceptually this is pretty cool! I really like the use of the small palette restriction and the vibes of each level were great. The only bug (i think) I ran into was that once I got to the third level, none of the enemies aggroed so it made it hard to find any of them without using the scanner.
A little bit of feedback to consider: The gun has travel time when you begin shooting and shoots immediately as you click, so your first bullet or two almost alway fly off to the left/right instead of directly in front of the player. This wouldn't be as much of an issue if the player had unlimited ammo, but in the 3rd level specifically I ran out of ammo so I couldn't defeat all of the enemies, and it didn't seem like there was another way to progress. Maybe making the gun snap towards the center would help once someone starts to shoot. I think that also adding a slow, but passive recharge to the scanner might help since I don't think I ran into any battery pickups.
Great job making this, it's super unique and it has a lot of potential for expanding on the idea!