Implement recommended thread access to prevent error spam on startup

[isirode]

Hi,

The PR as requested.

I removed the thread safety check, since it does not seem necessary anymore.

I tested it on 4.1 official [970459615] (downloaded recently), on a game with multiple scenes, the errors are not present.

Have a good day,

• Maintainer edit: This closes https://github.com/godot-extended-libraries/godot-debug-menu/issues/11.