Are there rules for the expense to maintain libraries? It seems odd laboratories are a separate expense but not libraries
There is not, AFAIK. Labs are a special item, because they are really expensive, eating up a large part of covenant budget. Presumably expensive ingredients are consumed during lab work, and the exotic specimens and tools magi use require special maintenance.
The maintenance of a library comes down to repairing books, the cost of which is not noticeable unless you want to spend a lot of work doing an economic simulation. I'd say it's covered by the cost of writing materials used by the scribes, who do that in their spare time.
I imagine at some point in most covenant’s summer stage, someone is tasked with making a library that protects the books.
Yeah. Covenants, p.66 sets the price for "Writing Materials" as "1 pound for every magus, scribe, bookbinder, and illuminator". And the latter three are the specialists you'd need for book repair anyway.
If a covenant has a significant library, but does not employ non-magi in book-making crafts, it would be entirely reasonable for the Storyguide to do something like randomly roll to determine if a book has suffered some sort of damage (from whatever cause) that didn't get noticed/repaired.
Spitballing, say, at the beginning of the first season a character starts reading a book, roll a stress die against Ease Factor 1 to find out if the previous reader or some other cause (pests, careless covenfolk, weather damage, whatever) damaged the book. (We're assuming that such incidental damage also happens in covenants which employ book craftsmen, but the specialists repair the damage as a part of their normal duties.) If the roll fails, reduce the book Quality by 1; if the roll botches, reduce it by 3. Raise the Ease Factor for the roll if the covenant is also economizing by skimping on storage and basic care for books relative to the standards for libraries outlined on Covenants pp.92-93.
Really good idea