Which EU law would that violate? Especially since EU is lately very sensitive about digital abuse.
Large vendors (gatekeepers) are not allowed to give themselves benefits that their competitors don't have. A third party alternative must have the ability to compete with the gatekeepers, which means Google isn't allows to treat Google Maps specially, Apple isn't allowed to treat Safari specially, and so on.
They can still comply with these laws if they have a quick and accessible method of getting your app store listed in the exemption list (which would quickly run into edge cases from apps like Aurora and the abusive shitstains that install stalkerware), especially if they show their willingness by pre-populating the list with common Play Store alternatives. They could also just disable the feature in EU phones (the way Apple chose to comply with the law) so they don't break the law. Or they could leave the list unpopulated inside the EU, making the OS harder to use for EU users but not exempting themselves as a middle finger to the EU lawmakers (the way Apple tends to comply with these laws).
If this works anything like other prompts of this kind, this will only appear for apps installed directly from an apk file, but not via apps installed from a store, even if the store itself was installed through an app file.
In principle, it would be possible to create a store that installs apps from the file system, perhaps with some affordances to enable automatic updates from a URL. I don't think it could support app files directly, there are some extra requirements on store "bundles", but an "installer" should be possible.
> Digital Markets Act, a 2022 law that requires Apple to open iPhones in the bloc to competing app marketplaces and alternative payment systems for in-app sales.
Do you think Google will allowlist fdroid?