I’m also curious about this. Say you install a non-Apple App Store app in the EU, then you go to Turkey, what happens to the app you installed? Does it stop working? Does it get updates? What happens to the alternative store?

It already doesn’t do this. You can stay on the app store you are on, or switch to the app store for the country you are in.

You can even temporarily switch, install a bunch of stuff, and switch back, but doing so is extremely onerous, as I think you need to cancel all your existing subscriptions and payment methods, as well as empty your balance (not sure of specifics, done it exactly once years ago).

Currently the only requirement to join an app store is to have a valid payment mean in the store country (including gift card I think?)

Most people I know juggle multiple store accounts (one in each country) and switch the app store account when they need new apps only available on the other side.

At present yes but there were some rumours that Apple was going to apply strict geofencing to the new changes, over and above what they currently do, for example using GPS to ensure you are in the EU.