That's Bluesky. It's supposed to be a federated social media, but right now there's only one kind of software for it and you can't yet self-host it (although you can self-host your data). The open-source protocol, known as AT, was created by Twitter back in the day, and Jack Dorsey and a bunch of staff were able to rescue it when Musk took over.

AT does not federate with ActivityPub, but users of either protocol can appear on the other using Bridgy; and some Friendica instances have basic support for AT. The equivalent of "fediverse" is "ATmosphere" (with the first two letters capitalised).

Since it became public (as opposed to invite-only), Dorsey left the platform and went back to Nostr (yet another microblogging platform, this time built around blockchain :-P).

It's actually quite a nice place, in my opinion, with a vibe similar to a combination of Twitter and Tumblr.

Sorry for going into this much detail. I just really like explaining things.

EDIT: Turns out, the word being thrown around in place of "tweet" was also slang for cum. I have removed it, as this was probably originally a joke.