The only rational response from the EU is to ban EU companies from storing EU data with American companies.
There is already a process now for Schrems III
I am liable if personal data pertaining to EU citizens is disseminated outside of the process set out in EU directives and local laws. This process does cover a local court compelling me or a local company to hand over something, and so in that case I will be in the clear. However, it does not cover the situation where I store my data on AWS and a non-EU court (US) compels Amazon to hand over the data, so in that case I will be liable for massive, potentially company-ending fines.
People have still not adjusted their behavior to account for the changes in laws, but right now it is very inadvisable for any EU entity to store any personal data on any service provided by a non-EU entity.
Think about how many EU jurisdiction entities use AWS. You think none of them are compliant? That's ridiculous.
Since you're the one with the claim - explain exactly which laws and treaties make it illegal to use AWS.
It all works because the public are made to believe these are good because they seem to go after some boogeymen (the evil foreign tech companies and the United-States).
The American CLOUD act grants certain agencies the right to demand data stored in European countries from American companies. This means American companies can either choose to comply with American law, providing said data, or with European law, refusing to provide the data without getting European courts involved. Refusing national security demands from the American government becomes very problematic real fast, especially when gag orders are involved, so companies and American citizens simply cannot be expected to comply with European law.
This choice has the consequence that American companies cannot be trusted to process PII (which is very broad) in any legal sense. Whether or not those companies go evil doesn't matter, the problem lies with the legal protection implemented by the American government.
I'd expect a CLOUD act equivalent from the EU (forcing companies with American offices to hand over the data of American citizens to secret European courts under the guise of national security) will be met with significant protest across the political spectrum. In fact, I would be disappointed if that wasn't protested. Surely Amazon, Microsoft and Google would be pressured to split off or shut down European operations if American citizens would suddenly become at risk of being spied on by foreign governments. If I were an American citizen, I'd certainly want politicians to do something about it!
GP's advice is solid. Avoid US cloud services for handling any private data.