once you have the catgirls and immortality, in what sense does she need the apologetics?

Whatever sense she likes (in addition to whatever sense you were talking about). If the nature of existence (and possibly the machinations of a rival god) are such that anyone who does not spend three hours in the apologetics library will end up not believing in her (and lose the benefits of affiliation) then I'll spend three hours a day in the boring library. If she actually physically requires the presence of the apologetics library in order to sustain her existence then I'll fight to the death to defend it. (The temporary death. Because I'm immortal. With catgirls.)