There sort of is although I don't know why anyone would want it.
There seem to be two problems with replacing Instagram or Twitter. The first one is money to run servers, fight spam, handle subpoenas, etc.
The other one is having an authoritative directory. How is anyone to know that "ClearAndPresent" on Twitter is the same as "ClearAndPresent@SomeRandomInstance.mastodon"? An obvious way would be to send a DM to a Twitter account but it seems likely that Twitter would shut that down pretty quickly. We've all heard the stories of Facebook (and LinkedIn and ...) pillaging Gmail for contacts.