The mutual friend is such a powerful signal, it is interesting that all that data is public, yet we have not properly utilized it.
Discussion
make a mutual algo relay to toggle on/off in global for a recommended mutual feed
This signal can be attached/used on many places, on user profile, likes, or even replies. It will really help user to find like minded people & it's meaningful!
Here's a great UI example.

It's great in communities like this, but in bigger communities it just becomes noise again. Look at LinkedIn with its "super networkers" :(
I think invite only federated instances/nostr relays might be a good compromise, maintaining quality and the town square feel without creating perverse incentives about friend counts.