How much control do we have over CPT rewrite slugs? Can I create a “root” page for my CPT with out the page path, and then have paths for other pages?

Say I have a CPT called I dunno, "Library" which is just a set of "pages" ("has_archive" => false) and the rewrite slug is "library". I also intend to have a set of pages like "about", "archive", and "new books".

Can I do something so that I make a page called "home" and instead of its url being https://example.org/library/home could it be https://example.org/library? And then the about page would have the url of https://example.com/library/about

And if I made a second CPT, "library-books" would there be away to set its rewrite slug to "library/books" or would I need a totally different path? so I would want https://example.org/library/books to be the archive for the "library-books" CPT and then https://example.org/library/books/book-title for the individual book posts.