Adding to what others have told you (social_facility=nursing_home), you should be aware that “nursing home” is not the translation of “Seniorenheim”, it translates to “Pflegeheim”.
There are various other tags for “Seniorenheim”, because there are different kinds of these and our tags are distinguishing some of them on the “main” level.
Other tags that might be interesting to find relevant facilities:
https://wiki.openstreetmap.org/wiki/Tag:social_facility:for%3Dsenior
(combined with group_home and assisted_living social facilities, and possibly others).
https://wiki.openstreetmap.org/wiki/Tag:amenity%3Dretirement_home