Most cars I’ve been in newer than 2015 or so can automatically switch their radios between FM and DAB, some smoother than others. So the technology must exist, but I don’t know if its available in freestanding radio units.

I’ve been using infomaniak for a while which suits my needs pretty well. It’s mostly intended for businesses but it’s very usable as an individual. Lots of storage for a decent price too and has all the functions you mentioned. Hosted in Switzerland.