Don't know about the US situation.
It would be one thing to, let's say, get vaccinated with a non-approved vaccine and claim damage, otherwise, unless, let's say AZ is excluded and maybe simply not "preferred" then it should be ok - as per 1. 1. which ok uses "empfohlen" (recommended/endorsed) so maybe it could be argued but I think it's more in favour of being in the scope rather than not
The Laender (states) may also recommend a vaccine, deviating from the federal STIKO recommendation. But they didn't really do that either, the wording is always very unclear and weasely around AZ. In several press statements, the phrase "auf eigene Gefahr" (at your own peril) has also occured. So I would wait for a clarification.
Edit: medical professionals seem similarly confused about the matter, KVNO is very roughly speaking a doctors guild: https://coronavirus.nrw/haftungsausschluss-bei-impfung-mit-a...
