Unfortunately, even if all data lives in the European Union, as long as a company is conducting business in the US, the Cloud Act makes it possible to compel them to hand over any information. This can include making administrative personnel sign NDAs or face heavy repercussions. Conducting business in the US includes advertising to US citizens e.g through maintaining a website in English.
At this point it’s unclear what a future digitally sovereign infrastructure should look like. Even if a company or a European state somehow manages to store data that is out of reach for the US Government, an amendment to FISA or the Cloud Act is something that any Congress should be able to put together.