I wouldn't become fixated on finding a specific term, especially not one linked to the provision of running water. The source only says "utilitarian spaces such as bathrooms and kitchens". To me (though with no special knowledge in this field), a cupboard under the stairs would count as a utilitarian space.
See, for instance, this (slightly pretentious) website:
... Give me all things utilitarian, all things whose primary role is about action. [...]
Our offices, our spaces dedicated to work. Where we do laundry, and where we take out the trash. These spaces can still be inspiring [...]
When designing any space that is ‘utilitarian’ in nature. Made for work to be done - offices, rest rooms, locker rooms, etc. I begin by examining the space as it is. ...
https://leslietylerdesign.com/blogblackhouses...
Of course there may be a German term for "utilitarian spaces". Perhaps "Zweckraum" is it -- I leave that to the native German speakers. Otherwise one could just give a description conveying the idea of "spaces which primarily have a practical function".
