Greek was the language of most fields of learning besides law in the Roman Empire. But the Greeks themselves wrote works on these papyrus scrolls that crumbled fast, so anything not actively used by the Romans was quickly lost.

There's a good chance that if the papyrus scrolls in any library (Alexandria or otherwise) weren't being copied regularly they were crumbling even before they burned or were lost to time for other reasons.

Towards the end of the Roman Empire, a few philosophers took the time to transmit Greek knowledge in Latin as knowledge of Greek faded in western Europe. What these guys happened to translate was the basis of most of European learning in philosophy, math, and other fields for centuries.

But they weren't monks (the most famous, Boethius, was not Christian either but a lot of later writers thought he was), the monks in scriptorium came later and grew slowly.

St. Benedict said that monks should be taught to read and do so regularly, which required copying books, but he prioritized physical work (to create self-sufficient communities) and prayer. But future Benedictines responded to the incentives of the time and began scaling up the copying and doing less agricultural work as the years went on.

That's the stuff that tells us how societies and cultures really worked.

I imagine that the Library of Alexandria was plural and diverse with respect to the traditions and inquiry that was represented there.