If you are concerned about private accounts on a server that you control (alone or in a group you trust), the Fediverse is the place for you.
Mastodon accounts can be private if you want. Same with a lot of other Fediverse software.
Try joinmastodon.org to get an account or set up a server.
If you currently use Bluesky, you can follow the same people from the Fediverse through the Bluesky bridge; but from a private account on a server you have some say in.