Private State Tokens are Google's implementation of the IETF Privacy Pass protocol. Apple has another implementation of the same protocol named Private Access Tokens. Mozilla has taken a negative position against this protocol in its current form, and its existing implementations in their current forms. See here for their blog post on the subject, and here for their more in-depth analysis.

The web needs ways to establish and convey trust signals which show that a user is who they say they are

Because it's just a convenient way to track people, confirm they are not bots, so that information can be sifted and sold.