Onto impressions! I was a little disappointed the character came from an asset pack, but it fits well with the environment and I like the atmosphere - so that doesn't matter. (and I would really love to see that ledge grab)
I have one issue with the background and that's the parallax moving faster than the foreground. To create the illusion of perspective the background usually scrolls slower than the foreground. This way around it feels a little disorienting, as if you were moving in a tight circle with the pivot point in front of the screen (in that case the background actually scrolls faster).
And a technical thing: some foreground tiles don't scroll properly on my machine and frequently show horizontal gaps:
I really like the slow and deliberate controls, but they are going to be extremely unpopular if you don't polish them up a whole lot. Like adding a ton of move cancel options (like you already do for attack out of landing - I'd expect to cancel most things with a roll or jump for example) and input buffers (like still jumping again if you start to press and hold jump while falling/landing instead of requiring to press afterwards).