Not the OP, but I alternate between self-hosted instances of Outline (https://www.getoutline.com/) and Nextcloud (with Collabora) for this. Outline I actually like better than Google Docs for most things. Nextcloud is a little rough, but it has change tracking, which I need sometimes.

I’ve also seen a lot of people using Cryptpad recently, which I think wraps OnlyOffice.

I think https://typst.app/#start has multi user support, you'd have to learn typst though

> I wonder what OP is using instead of google docs for live co-authoring

Probably nothing? It’s not like that’s a need that everyone has.