Hey, I'm new to Godot and never used the built in pausing. The way I do pause my games may solve your problem. I create a gdscript as singleton and there I put a bool called "running" and I also create functions to manage it, like this:
Then, in any script I use
if get_node("<path of your singleton>").get_running:
before any functionality to allow or not it to work
Hope I may help :)
