Fun game and creative concept. : D
I don't know how exactly Godot physics are implemented and are applied here so ignore if not applicable:
It looks like the scaling is allowed to happen independently of collision checking (i.e. scaling happens first and only afterwards collides with other objects/wall). The unintentional movement of the objects seem come from collisions with the player/wall, that push the objects in a certain direction. If that is the case, I think it would be good to resolve the collisions directly while scaling and explicitly solve for the correct new position (note: this also requires recursively solving the collisions of objects moved by the scaling, such as the player). And if no non-colliding solution for this position exists, to disable the scaling.
Viewing post in Purgob's Size Heist jam comments
I don't know how exactly Godot physics are implemented and are applied here so ignore if not applicable
Funnily enough, Godot's 2D physics got a pretty major update literal days before the Jam. (Not that I was skilled enough for it to matter)
That said, I'll look into it! Thanks for playing and the feedback!