Is there a browser-only JavaScript solution to unlock a password-protected PDF?

The LibPDF project claims to support encryption. Your attempt with pdf-lib failed because that library explicitly does not support encryption at all; the API is a stub. In general browsers won't (can't) do anything to prevent a JavaScript tool from being able to encrypt or decrypt content.

The docs for pdf-lib specifically say it does not support encrypted documents:

https://www.npmjs.com/package/pdf-lib#encryption-handling

pdf-lib does not currently support encrypted documents. You should not use pdf-lib with encrypted documents.

Mozilla's PDFjs, however, does seem to support working with encrypted PDFs; though documentation and examples are limited.