temporarily move in another country, accessing Local App Store

Apple's media and app purchases are licensed on a regional basis. Apple does not accommodate people who claim to have dual residency. Many people would like to violate the terms of use by using various methods but even setting up a second account. The route that Apple provides is to change country settings on your account, but of course then you are restricted to what is available in the other regions. --> Change your Apple Account country or region - Apple Support

You can try setting up a different account but you will face various hurdles. You will have to have a complete set of address, payment, and telephone numbers for each country. When setting up an account in a country you are legally declaring you are a resident of that country and this would appear to be Apple's way of confirming that. Also note that this works best if you have two iPhones. Apple places restrictions on frequently changing accounts signed into a device.

View and remove your devices that are associated with your Apple Account for purchases - Apple Support

‘When you try to associate a device that was previously associated, you might notice a message that says, “This device is associated with another Apple Account. You cannot associate this device with another Apple Account for [number] days.” You might need to wait up to 90 days to associate the device with a different Apple Account.’

The only solution is the one your tried, a separate account for the EU country, or to constantly change the region back and forth with your current account.

Change your Apple Account country or region - Apple Support

Changing the region back and forth has it's drawbacks. Make sure that you have updated all your apps for Region A before changing your account to Region B. While you are registered in Region A, you will not be notified of app updates for apps exclusive to Region B and vice versa.

M1 Mac mini, macOS 26.0.1;  Watch, Series 10 GPS-only, watchOS 26.0.2; iPhone 16, iOS 26.0.1; TV 4th Gen, tvOS 26.0.1 HomePods, audioOS 26