This is highly problematic.

I may consider showing my ID to a company I already have a business relationship with; given demonstrable legal obligations, contractual necessities, legitimate interests etc . Eg the standard GDPR list.

I do have an existing business relationship with Anthropic, so I might under some circumstances decide to show them my id. I don't have a business relationship with Persona though.

I understand the instinct: they want to insulate themselves from holding PII. Not the worst idea. I'm not happy with it being a third party though. Especially the third party in question.