Very original idea! I especially like the fact that most levels allow for creativity and multiple solutions. Unfortunately it's easy to lock yourself in by accident, as precise movement is really hard without being aligned to a grid. I don't think however, that you should align the character to a grid: it would make the movement feel clunky and restricted, whereas now it really is a free form jump and run. Maybe add a limited amount of undos though to mitigate the frustration of fails shortly before the exit. Speaking of exits: I would have liked if the exit position in each level is clearly marked in the start (without being active of course) so you can plan your route accordingly. Also I found the black tentacles (?) appearing from level 3 onwards a bit irritating at first: I assumed touching them would result in a fail, but realized later, that's not the case and they are just there for decoration. Consider redesigning these. Overall great puzzle game though, fits the theme well and is quite a bit more innovative than mine.
My puzzle game: https://njamster.itch.io/wonkey (playable in browser, not mobile friendly)