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.
Another issue here is that their DPA frames everything as controller-to-processor, i.e. they do not appear to have SCCs in place to actually receive this personal data as controller. So the original exporter would likely also be in breach if they send any GDPR covered personal data to this model.