Mainly relates to eBooks now;

https://goodereader.com/blog/e-book-news/here-is-a-breakdown-of-how-much-libraries-pay-for-ebooks-from-publishers

Edit; found a good summary.

Libraries pay more for books than a customer would at retail.

There are different payment models libraries use. And not all options may be available to all authors.

The one-copy method pays for the book up front, while the cost-per-checkout method pays a small amount each time (and can be more profitable in the long run).

With the one-copy method, libraries often pay two or three times the retail cost of a print book—and sometimes even more than triple the retail price of an ebook.

With the pay-per-use model, a book makes an amount less than the retail cost—but each time it’s “checked out,” the author gets royalties. If a lot of people read your book, you win!

Source; https://danieljtortora.com/blog/are-libraries-good-for-authors#:~:text=With the one-copy method,%2C” the author gets royalties.