The way Apple Health exchanges data with 3rd-party trackers (Fitbit, Garmin, etc.) is very well built and a good model of how other components in iOS could allow data exchange with very granular permissions.
Apple touts the "Private Cloud Compute". If they found a way to share your personal context to process on their cloud in a private and anonymized way, there is no reason the same process couldn't be used to handoff data to a 3rd party AI provider.
One of the issues here is that there are many people with strong opinions that don't understand the thing they have strong opinions about. Which is the normal state of human affairs.
It looks like Apple is framing this as a privacy issue as a marketing tactic so that consumers will blame the EU when Apple COULD implement it without endangering privacy.
You don't seem to know how backdoors work.
Oppressive regimes mandate that tech companies pre-install apps to protect people from spam calls, or install specific root certificates so they can intercept your traffic and insert a helpful banner into your browsing session to remind you when to pray.
The EU isn't going to ask Apple to add DataCollectionBackdoor(). They are going to demand that in the spirit of freedom and happiness EU companies must have access to Apple users private data.
You want Apple to anonymize a users data, then hand that users data to a third party who knows who the user is? I don't think PCC is doing what you think it's doing.