John Debney and Joseph Trapanese are credited with the music composition.
I guess just underscoring is considered in the Score category. Pasek & Paul did not share in Justin Hurwitz’s Best Score Oscar win for La La Land last year.
But Pasek & Paul didn't even write the music for the songs, which, yes, are not considered in the "score" category for the Oscars. So they wouldn't even have been eligible for it even if the songs were included in the "score".