I had this issue back in Godot 3.5 and hoped that it'd be gone, but Panels and some other Control Nodes still resize magically when executing another scene. This is such weird behaviour, that I have no idea where it might come from. Has anyone ever seen such a thing happen before? Here is a video of the bug in acton: https://piped.kavin.rocks/watch?v=79DYDT5qngk
If you recreate the issue in a new project with only the needed nodes and it's still happening then it's more likely to be a bug than something you've done. After watching the video I'd suspect there is a bug because I don't think it should change like that. If you can better understand when the bug happens then you may be able to find a bug report already exists.