One very important point here is that it looks like Anthropic is becoming GDPR controller for all submitted data. So data subjects have Article 15 right to request information about processing and possibly a copy of the data. Latter might be contested under "rights of others", but former is more absolute.

What this means it that if someone makes an Article 15 request, they would be entitled to know if Anthropic holds personal data about them and also from who they received this data at minimum.

If someone wants to do that, I would recommend combining it with Article 18 request to forbid deleting the data for legal claim in case you contest Anthropic's reply. Otherwise they could just delete the data per their retention policy and DPA would find much later that they no longer hold the data.