Very cool demo! I've played on linux on a controller and it overall worked great. Pressing down to slide on the controller doesn't work, but the dedicated button (RB) worked. All the cool stuff for a good platformer are there: solid feel, expressive mechanics, etc.
At first I had some troubles getting used to the movement, mainly on the wall. It was tricky to initiate wall running (it's a fun mechanic btw) and I expected that when I press dash when sliding on a wall I'd dash away from the wall (I think that's how it works in Hollow Knight and maybe Celeste), but it didn't do anything.
Those flying things that you can hook from could maybe give an indication on the direction that you will be launched in?
I also felt like the controls were a bit slippery for the amount of precision required on some levels (e.g., breaking distance longer than a platform on which you need to land).
And I also would expect those bouncing platforms to renew the dash, especially those on the ground, since it's kinda like touching the ground.
After I completed the demo I found the entrance to the first level and flew through the levels with ease, which was really fun! So the potential is definitely there!
For the future tutorial I'd give player more time to get used to mechanics before giving new ones, but I understand that you needed to cramp things in a short demo.
The art and especially animations and effects are also very good.
Please continue working on this!