Thank you so much ! Here is my move and slide function right now :
velocity = move_and_slide_with_snap(velocity, snap_vector, Vector2.UP, false, 4, PI/2 * 0.7, true)
I had tried to with stop on slop true, but it's even more glitchy and the character never slides, which feels very weird on steep slopes. It would be nice to be able to control how slippy the terrain is.
The problem with the jump isn't actually that you can't jump, but it seems that you're jumping in two different directions at the same time when you are in a corner, which kinda cancels it. Now I am thinking about it, it might be due to my jump function, that's not working properly if there are multiple floors :
velocity += get_floor_normal() * jump_speed
Thanks again for the great explanations ! I'll try these ideas and others you gave me.