Pretty good. Some countries like Slovakia built cycle ways on the levies.

The EU also pours money into bicycle touring: They design and promote the Euro Velo routes (signposts). I believe they run a few campsites.

But there are other reasons why the Danube is the most popular bicycle touring route in the world: It's flat and it passes through many cities of great historical significance.

I also like to stop and chat to other cyclists when I see them and that occurs frequently on the Danube route.

Between Passau (Germany-Austria border) and Vienna, you have asphalt for most of it, with some unpaved/compacted parts (it may have improved since 2015). You need to cross the river by small boats (for a fee) a few times. For bicycle touring, checking the type of surface on OpenStreetMap beforehand can be quite useful. Travelling on unpaved paths is not at all as fast as on asphalt is you have an hybrid bike (my case).

you can stick to these routes if you wanna cris-cross Europe

https://en.wikipedia.org/wiki/EuroVelo