So write it locally in an unshared document and paste it into overleaf when you want someone else to see it? I don't like overleaf to begin with, but to feel this tied to it is a bit wild.
I've tried, but it only works well if it's the beginning of a project. Later on, it gets annoying to sync back and forth between copies as others work on it, since I like to see what I'm writing in the context around it.