Just so you know, "move to Europe" is pretty complicated inside Apple ecosystem. You can't move your App Store account from one country to another while you have any subscriptions active. You cancel them, wait for them to expire, and only then you can switch. So, for example, if you subscribed to an app yearly in January, and then cancelled your subscription in May, you still have to wait until January of next year. Very annoying in practice.
It's easier if you create a new apple ID which you use for the EU, separate from your existing one, and then login to the phone with your old Apple ID, and login to the app store specifically with the new one.
As a bonus, you can then re-buy all your apps if you want to not have to sometimes toggle between the old / new one to re-download already purchased apps.
Frankly, I'm surprised apple doesn't hard-require you to re-purchase all your apps when you switch regions, it would be a lot more apple-like.
While Apple has technically permitted third party browser engines in the EU, they have made it so onerous and expensive that no company is likely to build one. Apple remains the gatekeeper and will likely deny any builds for many years while they abuse the EU courts in delay tactics.
The EU has been fumbling the application of the Digital Markets Act. They have been sitting on a judgement of non-compliance regarding third party stores for literally years now. By now they could have moved to forced compliance and huge fines. It's not clear if there is some kind of hidden diplomacy happening, a desire to not anger Trump, or sheer incompetence. Either way, I have lost hope that the EU bureaucratic engine will ever do anything to help ordinary people. Their only function now appears to hurt the very weakest in society, because they can't fight back.