> How that works, especially with freedom of movement from the rest of the EU, is anyones guess

This was already answered. Germany has a welfare-system which is basically a restrictec UBI, and there were non-german eu-citizen demanding access to it and went as high as the European Court of Justice.

Result: they have no right to claim social welfare outside their own country. Freedom of movement in EU has limits and you must behave like a proper local citizen (like working there for some time) to get access to other countries systems. And even then benefits are time limited.