Depends on the identifier.
If by identifier, we mean “account identity” (authentication), then VPNs like Mullvad & Windscribe tell us that they keep them separate from their data plane.
If by identifier, we mean enrolled keys (authorization), this is the part where the user is in full control. They generate the configs and rotate them as and when they want to. Besides, in our example, Mullvad has no knowledge of the keys used for Windscribe & vice versa. This is strictly better.
Privacy Pass is a cryptographically guaranteed way to keep authentication and authorization separate. It changes nothing (in terms of privacy), if we already trust Mullvad & Windscribe to do so.
True. In a single party setup, it doesn’t make much sense to implement the full RFC (just the blind tokens part may be enough). In a multi-party setup, Privacy Pass provides an avenue for one VPN party to let the client (end user) anonymously enroll with the second VPN party. It doesn’t really change anything wrt WireGuard and its key generation & key exchange mechanisms (that is, the “identifier” must be ideally rotated even in this setup; or, the providers use MASQUE instead).