Is it possible as a pilot to get the ICAO proficiency language level for a not official language in the ICAO?
As the others pointed out, there's no ICAO language proficiency test for German.

How it works for German at least in Germany is with a special "Radio operator license" (Sprechfunkzeugnis) that's part of (German) pilot licenses. For IFR that's only in English, but for VFR you have the choice of doing it in English, German or both. It's called BZF I (English + German), BZF II (German) or BZF E (English). According to the German Wikipedia, there are similar systems in place in Austria and Switzerland.

Even for VFR in Germany it's totally possible to do it in English, as I believe there are no more German-only speaking airfields. But especially on smaller fields where radio services are provided unpaid by people in their free time, they are a bit happier when using German.

And even on the bigger VFR fields with professional ATC personnel, my experience is that it's sometimes hard for them to remember, which aircraft in the pattern is communicating in English and which in German and then they try to translate position reports they get in one language from one aircraft into traffic advisories for other aircraft in another language. That's why it's sometimes recommended for pilots flying more often VFR in Germany to maybe also do the BZF in German as most VFR traffic is still done in German.