Observations as I played:
Music is loud and the slider in the options menu doesn't do anything. Nor does toggling sound sfx, seemingly (the button is permanently 'on'; clicking it seems to select it rather than actually toggle it?)
Could have done with a prompt for which button to press to start the game in the map screen
Vertical parallax with the background/foreground elements is honestly too strong for me; it looks more like elements moving up and down on their own rather than a perspective effect. The vertical movement itself is too strong in relation to changes in the player height, the treeline graphic in particular seems to 'float' above the world, leaving cut-off parts exposed that probably aren't meant to be visible.
The foreground object in particular looks very similar to the actual playing area, so when it moves it looks more like a rising platform; it's pretty visually confusing.
Tl;dr look into how other games handle these things, f.ex try making the foreground darker, blurry and indistinct to clearly, visually separate it from the playable area. Similarly, you could make the mountains look more 'distant' by way of atmospheric dispersion/fog pulling them closer to the skybox's colour.
Mouse cursor being a sword keeps making me think I'm going to issue an attack order when clicking. That's probably just me though.
Near impossible to climb with an xbox controller. Much easier to play on mouse/keyboard. On a related note, there is no jump button for people with xbox controllers. I'm guessing you're using Unity's old legacy input? Controller mappings are a nightmare with that; I strongly recommend switching to the new Input System, as it solves a lot of that tangled mess.
On the first climbing wall, actually stopping on top of it for the coin is uncomfortably difficult as you zoom over instantly given in the instantaneous velocity you get whilst moving. You speed up instantly, but you actually slide about if controls are released, resulting in very slippery movement that's difficult to control. If you want to dig in on 2D platformer controls, this Gamemaker's Toolkit video breaking down how Celeste's movement works is an excellent start.
Sometimes she summersaults when jumping and sometimes she doesn't, and I'm really not sure why or when.
Died constantly just trying to grab the handlebars on the first hazard, because of the slippery controls. Eventually just gave up, took the hit and continued, which is probably bad tutorial design if you wanted to teach about the overhead bars.
I think she's trying to climb over very short obstacles. Like again, the first hanging bars, there are two small steps just in front of it. Push up against them and she goes into the 'against wall' climbing pose. This almost makes actually stopping on the last step difficult, because she keeps doing that climbing thing when she reaches the top of the wall and zooms off... into spikes.
Overhead climbing is as fast as walking. Feels weird and definitely doesn't match the climb animation.
The sword attack animation pushing you backwards is a very strange choice. Combined with the slippery keyboard controls it's definitely not fun. How far back they get pushed also feels very erratic and inconsistent.
Pretty sure I broke something at some point: enemies were just walking into me and dying. I suspect the damage trigger on the sword didn't deactivate. I was constantly getting pushed backwards too. Attacking again reset this, and I wasn't able to reproduce it. I assume activating/deactivating the attack box is based on events in the attack animation? Presumably, something interrupted it inbetween those events. If you're using AnimationControllers, you can addstate machine behaviour scripts that - amongst other things - can run code in OnStateExit to always close your attack boxes when it leaves the attack animation which would solve this issue.
It's not too obvious when you take damage, or how much health is left. I died a couple of times in the trap-house and often didn't understand why. It's a matter of visual feedback, mostly, it's easy to miss the player flashing red if your attention is elsewhere and the healthbar is pretty small.
The audio in the trap-house is odd. The sounds of the traps are at a constant volume, rather than increasing/decreasing as you approach. I honestly thought it was an audio bug at first.
Unfortunately I was unable to progress much further than that between the deadly traps and slippery controls, so I can't comment at all on the rest of the game.