@zungryware I was playing on Firefox. Tried again on Chrome and didn't notice any issues with the mouse or player movement. I can understand why that fixed the mouse issue, based on your comment, but I have no clue why the movement jank also seems to happen on Firefox and not Chrome. Maybe the browser messes with the frame pacing or something? My computer should be more than overspec for this game, so if anything my framerate would've been too high if that was the issue.
I also got further, thanks to those issues no longer being there, and I can definitely say the second pistol makes shooting feel better. It's kind of a slow grind until you get one, though. On the jetpack recharge, I think I didn't notice it my first couple times playing because it recharges so slowly that I didn't realize it was there, even with a battery (not sure if batteries stack, I only sprung for 1). I do also think the jetpack drains way too fast, especially given how extreme the gravity is. Making what seems like a small jump to grab honey got me killed more than once due to how fast I ran out of fuel.
As far as encouraging the player to move goes, why not have the enemies shoot at the player's feet some of the time? They seem to be content to shoot parts of the ground where I'm not standing, which actually doesn't really punish me for standing in place and shooting them. At the same time, the environment can be destroyed so granularly that I'd have to be looking at my feet a lot to make sure I'm not going to fall into a player-sized hole and lose a life just for that. Maybe the environment could consist of fewer, larger pieces that take a few hits before being destroyed, that way falling to my death wouldn't feel as "random", if that makes sense.