I enjoyed the movement quite a bit, though I ran into a weird bug where sometimes my character would slowly drift on the ground without inputting anything.
The movement was a tad floaty as some pointed out, but I think it works well in a game like this with a bigger, more open environment.
It kind of reminded me of the old arcade game "Legend of Kage" (though your jump ends more abruptly at the peak height): (warning, some flashing lights in parts of the game footage if you are sensitive to that kind of stuff)
I was impressed with the enemy ai that floated around and shot at you. It felt well balanced!
Different footstep sounds on different pieces of the environment was a really nice detail!
Game definitely needs more feedback on when you hit enemies - it's hard to tell when attacks are connecting. I'd also increase the range of the attack a bit more. A lot of early NES games had the issue of stubby attacks that would often trade with enemies, so it's a classic problem that is tricker to solve than many would think.
Legend of Kage actually had this issue with it's melee attack as well - but most of that game you were using a projectile instead.
Attacking in two different directions with 2 different buttons felt a bit strange. I'd just keep it simple and map it to a single button (left click / "x" button (on an xbox controller and let the player control the attack direction with movement).
There was some weird tearing at times when I moved around - especially in the beginning. I would check out Cinemachine for your camera system if you weren't using it (it's free and has soooo many awesome options!). If you were, make sure to enable the "pixel perfect" extension. This often fixes these issues! :D
Whew, so I know that was a lot, but I think you have a good framework here and I wanted to spend the time to provide constructive feedback! I can tell you put a lot of work into this with some of the small details I found as well. Good work, keep it up!