Nobody cares if they call it ACR or not. They're not doing it. By any name.

Apple Intelligence takes a single screenshot of your screen when you explicitly direct it to. It does not take routine or scheduled screenshots and it does not exfiltrate or otherwise use the information other than to answer your query.

Private Cloud Compute goes to great lengths to prove it can't violate your privacy. In general, Apple likes to back itself up like this, which is one of the reasons I have such high confidence in them.