Cool demo! Thank you for making it. Some feedback:
Having the same key (spacebar) that you latch on to things also be the jump key is really cumbersome. Makes the platforming much less fluid and I'm unsure of what's going to happen, especially when you get the double jump. I would rather you just auto latch on to things like ladders (I understand ladders are really hard to get right in games but this would be preferable)