"Stewardship" might be the word we're looking for: it has some connotations of personally invested care, but it's also clear that it's done on behalf of someone

"Stewardship" might be the word we're looking for: it has some connotations of personally invested care, but it's also clear that it's done on behalf of someone else and there's no ownership. Of course, it also has a history of association with servants of landed gentry, which might make people uncomfortable (for good reasons, to the extent the analogy holds up).