Generally speaking, the design of the Fediverse leans towards radical transparency and disclosure.

It’s not particularly private at all. Instead it levels the playing field by making a lot of the data companies would normally be harvesting and selling available to literally everyone with minimal effort, drastically reducing its value. It also just collects relatively little data to begin with.

If, however, you were hiding from a hostile government or something, this is one of the last places I would use for communication.

Depends on the location of the instance. The EU and California have laws for that, for example.