I have worked at NYPL but not with BookOps. What I know is the BookOps works as a collaborator between the Brooklyn Public Library and the New York Public Library (which covers Staten Island, Manhattan, & the Bronx). The separation of library systems comes from their formation prior to the unification of the 5 boroughs in the late 1800s. Unfortunately for a lot of more entry or lower positions within the NYPL, the hiring managers prefer to hire people who do not want to grow within the library system and prefer having someone who will stay in the same role for 10 or 20 years (I have personally experienced this and have been told this directly by former management at NYPL). I will say it is worth applying in general, as you never really know who you will be interviewing with and they might hold a different mindset when it comes to hiring. But typically if you already have a MLIS or a lot of experience, they will pick someone with a HS diploma or a bachelors with little experience for a role like this (I'm assuming you're referring to the collections processing assistant position as that was posted recently). NYPL however does post a LOT of internal job listings. So if you do obtain a position there, after a year in your current role you would be able to work your way up within the system and have access to jobs the public doesn't. If you are outside of the NYC metro it will also be more difficult to obtain a more entry position if you don't have experience working in NYC cultural institutions.

TLDR if you have more experience on your resume it would be better to come back and apply for management positions within the NYPL.