This has come up a long time ago as a feature request Index public repos of gitea instances #7853.
There are a few well-known instances like Codeberg, but a real list probably won't ever exist because many of the instances are private.
The closest I am aware of is https://gitea.com/gitea/awesome-gitea#user-content-organizations
Generally we encourage self-hosting, so there isn't a huge drive for a public listing. Codeberg is the one I would probably point to first.
It's linked to from this list of third-party packages, which in turn is footnoted in the Gitea installation docs. So yeah, not exactly easy to find.
There's also https://gitea.com, which is going to be used by gitea for itself instead of GitHub like now.
It's hosted by a chinese company and I don't think they support Gitea except for hosting the "official" instance. Codeberg is definitely the better choice, starting from the fact they are a German non-profit that owns their servers and is in the EU.
>Gitea doesn't offer free hosting
wut
https://gitea.com (used by Gitea itself, but hosted by a chinese hosting provider)
https://codeberg.org (hosted by a german non-profit organization)