The art and idea are so nice that I gave the game a second chance despite the annoying controls. At first, I thought it might be the WebGL's fault, but the Windows version's controls feel the same.
If you plan to continue this or making another platformers, I suggest searching about "coyote time" and "jump buffer". These are just small bits of extra code, but they make the jumps super responsive.
Additionally, I think you should reduce the shake effect a little bit, a little shake when the character fall from height or when they attack is cool, but constantly shaking when the character doing every little jump can be annoying.