LibreOffice Writer online was not popular, so it is understandable you assume it doesn't exist. There is also the trivial headless Linux remote desktop cloud hosting with 100% identical functionality.
>"edit at the same time"
Perhaps you meant: "View -> Toolbars -> Track Changes..."
Most documents that support OLE have difficulty handling concurrent writes. Office 365 abandoned desktop publishing in 2019, and replaced it with a web document management system.
Best workaround is every user imports each instanced changes: "File -> Merge Document."
And manually handle any collisions.
I would post how to setup your own remote collaborative environment on an $8/month host, but people seem like they are not interested. =3