Let's say the library panics because there was an out-of-bounds array access on some internal (to that library) array due to a bug in their code. How will you handle this error yourself, and how is the library supposed to propagate it to you in the first place without unwinding?

Ensure all bounds and invariants are checked, and return Result<T, E> or a custom error or something. As I said, I do not want a library to panic. It should be up to the user of the library. When I write libraries, I make sure that the users of the library are able to handle the errors themselves. Imagine using some library, but they use assert() or panic() instead of returning an error for you to handle, that would frustrate me.