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I think the character is jittering! Maybe the position is rounded to full "game pixels" as opposed to sub-pixel movement?

Also it seems the linked Windows version runs a bit worse even :(

yeah, that's the Unity build and it is messed up in a different way :)

Regarding the jittering, I think it's because of the way I'm handling velocities of things bumping into each other -- the position is most definitely rounded to full game pixels, because otherwise the pixels would be hideous! but I'm not sure how to handle the case where pushing against something flickers you back and forth across the boundary.

In this HTML5 Godot build there's none of that weird subpixel rendering trash like in the Unity build, is there?

Yes, that trash is what I meant when commenting on the Windows build! I'm not seeing it in the Godot web build.

By sub-pixel I basically mean that since monitor pixels are smaller than "game pixels", we have the option of upscaling sprites individually instead of upscaling the whole scene (see here for examples: https://medium.com/@tumeowilliam/godot-engine-and-pixel-art-a-better-love-story-...). And this could help with getting smoother movement (this is not pixel-perfect, but during movement it's not obvious).