Do you happen to know about the high jump you can do in Hinedere Beat? I briefly skimmed through the runs and didn't see it used.

It should help you get to some platforms that the game requires you to do some extra work for. As far as I remember, it's only useful to get onto ledges, I don't think you can get to rails / pipes this way or run up a wall at the end but I'll leave that to you to find out.

The short description of how to do it is: Hold up. Jump. In the landing animation, jump and (what feels like) a frame later kick. To move left / right in the air, you'll need to let go of up.

This seems like the frame you want to aim for when doing the jump / kick:

Here's a short video with an input viewer: