Encrypted at rest or not, the hosting company could easily dump the encryption keys out of memory while the server is running. If you're an American citizen, the government can just directly go after you or your company. If American law enforcement can get access to the data (i.e. by plugging the server into a UPS and carting it out of the data center) you're violating the GDPR at the very least; both attempts at skirting around the lack of American privacy guarantees were defeated by the American government refusing to provide sufficient data protection laws for European citizens, after all, choosing to uphold the PATRIOT ACT (and other such laws) over the digital business of EU customers.
Something as simple as a database password definitely doesn't fly as far as I know based on reading through the GDPR. Maybe it's legal if you apply enough tricks, you should consult a lawyer if you want to know your workaround is sufficient.
However, by default, storing PII of EU citizens (+UK citizens, I believe, they've implemented the GDPR before they left) with American companies is not legal. I can see how in theory a remote disk drive with fully end-to-end encrypted traffic (encrypted inside the EU, merely stored abroad, the decryption key never leaving the EU) may be allowed, but if the data gets decrypted on the American end I'm pretty sure you're out of luck. Otherwise, any form of TLS would be enough to avoid the GDPR, and that's definitely not the case.
Encryption at rest doesn't protect you. In fact, may even be legally required, regardless of where you store your data. The GDPR doesn't specify any exact security measures, but you do have to try your hardest to secure any PII you may process or store and encryption at rest is one of the easiest steps you can take to do so. You should make a conscious decision of what data may leak to where, the impact of the leak, and ways to counteract such problems.
Something as simple as a database password definitely doesn't fly as far as I know based on reading through the GDPR. Maybe it's legal if you apply enough tricks, you should consult a lawyer if you want to know your workaround is sufficient.
However, by default, storing PII of EU citizens (+UK citizens, I believe, they've implemented the GDPR before they left) with American companies is not legal. I can see how in theory a remote disk drive with fully end-to-end encrypted traffic (encrypted inside the EU, merely stored abroad, the decryption key never leaving the EU) may be allowed, but if the data gets decrypted on the American end I'm pretty sure you're out of luck. Otherwise, any form of TLS would be enough to avoid the GDPR, and that's definitely not the case.
Encryption at rest doesn't protect you. In fact, may even be legally required, regardless of where you store your data. The GDPR doesn't specify any exact security measures, but you do have to try your hardest to secure any PII you may process or store and encryption at rest is one of the easiest steps you can take to do so. You should make a conscious decision of what data may leak to where, the impact of the leak, and ways to counteract such problems.