What tools do you use to manage writing co-authored papers?
The best option is Github I believe. But it pretty much depends on what do you use for writing papers? Do you use LaTeX or other typing softwares like Microsoft Word or LibreOffice which is the free and open source cousin of Microsoft Word. If you use LaTeX, which I recommend it personally and probably many other people here too, you could create a repository in Github and put your tex files as well as bibliography files and then simply you could share that repository among your collaborators. The reason why I like LaTeX instead of using Microsoft Word is that tex files by themselves are human readable files in comparison to binary .doc files. As a result, you could track and maintain your version control for your paper like a code. Otherwise it's not easy and trivial to track binary files (e.g. .doc files) by Github or other version control softwares (e.g. Data Version Control (DVC)) Also, it is possible to link that repository to OverLeaf and that makes sharing/writing much easier. But for more accurate solution in order to fulfill your needs you need to mention what is your main writing software for preparing papers.