I too have games now that are having their graphics and layout distorted because they can't handle resizing well. I think that the newly opened window should restrict its initial size to what's specified in the game's 'Viewport dimensions' option, AND that the new window should be created as non-resizable UNLESS explicitly marked as resizable (e.g. by providing some new 'Allow resizing pop-up HTML window' embed option solely for this purpose). Or if non-resizable window is not feasible, just restrict the size of the viewport in the new window too.
Anyway, it's great that you're looking for solutions regarding the SharedArrayBuffer problems related to Godot+Firefox as it's been a pain lately. I do hope that at some point these tricks won't be needed anymore.