Do you know if that affects movies bought through Apple’s TV app (US)? I have quite a few movies in my collection and would be really annoyed if they didn’t work in Europe.
According to this community post (https://discussions.apple.com/thread/253966277) that implies that DRM'd content is not available in those countries, and that you'll need to download your movies and for them to work depending on the country you're visiting.
If you're coming over for a temporary visit, setting up a VPN on your home network may be a good idea. Many American services are not available in other countries, even if you're a paying customer.
Streaming services will even edit or censor movies as they please.
https://variety.com/2019/digital/news/hbo-edits-game-of-thro...!
https://scribe.citizen4.eu/everything-80s/why-are-streaming-...
Honestly the only way to preserve most digital-only video media today is piracy.