Back in the day when Direct Connect[1] was a thing, and we all had insane speeds in the metropolitan area (but not so great outside of that), I used to run a DC hub. Which due to said speeds had mostly people that were close by, geographically speaking, and the interactions felt so much more relevant, probably because of the "third thing" you mention, the common interest/background.
So I've also been thinking for a while now: how can that style of community be recreated? There's of course the chicken-and-egg problem until you have traction, but also things like: how big should the community be, geographically? The same size in the US vs EU likely encompasses quite different amounts of people. Should it be anonymous or real identities? Should history be viewable by new members or should it be ephemeral? And so on.
Anyway, interesting prototype, I hope you get some traction!