I'm surprised nobody has mentioned the classical "token"/"cookie" system.
The way I used to write papers with coauthors 20 years ago was using an informal token system. If I wanted to edit Section 1 of the paper, even just to fix a single typo, I had to follow these steps:
- Email all coauthors with the text "I am claiming the token for section 1."
- Edit section 1
- Email all coauthors with their edited version of Section 1 and the text "I am releasing the token for Section 1."
Nobody was allowed to keep the token for any section more than some agreed limit. typically 24 hours, but that often shrank to 2 hours or even 15 minutes as deadlines got closer. In principle, everyone could keep their own local copy of the paper up to date, but in practice, it was helpful for one co-author to periodically recalibrate by claiming the token for the entire paper.
As long as everyone followed token discipline, there was no need to worry about file names. There were no version disputes, because the most recent version of Section 5.4 was always by definition in the most recent email releasing the token for Section 5.4. In particular, if you branched, it was your responsibility to merge correctly, not your coauthors'.
On the other hand, co-authors (including both PhD students and tenured Luddites) who didn't follow token discipline found themselves involved in fewer papers afterward.
While my paper collaboration has mostly moved to Overleaf+git, I do actually still use this system on the unavoidable but thankfully increasingly rare occasions that I need to collaborate on a Word document with someone who doesn't have access to Word Online or Google Docs.
tl;dr: Don't do this unless you have to.