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Is there a stable mature lightweight mastodon/PubSub server (ideally with sqlite storage) that's easy to maintain to serve a handful of users?

Can't give opinion as I don't use it but you can take a look at https://masto.host/

I meant software, not service

if there’s just a handful of users can’t you just share a note from the notes app, or is that too personal?

I don't see how a note from the notes app will serve as a maston server.