Do Cloud and Privacy Go Together?

I would suggest it depends on what mutually signed business to business contract you have in writing with those companies and what they/you agreed to and what the penalties would be for breach of contract.

Another thing to consider is 3rd party contracts. i.e. When your business outsources parts of your systems to yet another cloud provider, then your customers should be made aware such an arrangement exists, as that can in some cases make that 3rd party cloud provider a 3rd party data processor, depending on what data they have access to.

Disclaimer: I am not a lawyer but the above comes into play quite often in SaaS.

Are you under the impression that if you put data in GCP or AWS, that they are using it to learn?

Because that's not how it works, they don't look at your cloud data like they do your browsing activities. It would be a show stopper for their businesses. Google at least has audit logs to show when/why their engineers were touching your cloud resources.

Encrypt locally.