Of course that would also mean any authenticated video can never be truly anonymous :(

With modern face recognition, having your face in a video already deanonymizes you so there is no further deanonymization caused by authenticating your video cryptographically.

If you want anonymity then don’t include your face (or signature) in the video.

If you want attestation that a video is real and not generated then anyone who witnessed the scene depicted can sign the video to attest to it. Then we would need a web of trust to determine whose signatures are trustworthy.