A little bit confused by this. Is the idea that one is running an instance of LibreOffice on a server somewhere and interacting with one's own documents via HTTP that way (and does LibreOffice have a server built in? If so, this doc doesn't say how to start it or anything.)

From skimming a recent FOSDEM talk that was uploaded the other day [0] I think it looks like an open source web based office suite you can host yourself. There's also a dockerized version available [1].

[0] https://www.youtube.com/watch?v=kEVzth5etWo "LibreOffice Online adoption into 1&1 Mail&Media ecosystem Brief overview of the open-source adoption"

[1] https://hub.docker.com/r/libreoffice/online/

Am I overlooking something? There seem to be no instructions on how to start a server. Or does It always start a local server?

These are instructions for interacting with a running Libreoffice Online service.

This document looks like just the API spec.