How can I switch Music libraries on my MacBook Pro?

Music will open in whatever Library you opened last.

To change the Library, hold down the option key, while opening the Music App in Finder. It will request you select a Library or navigate to a Music Library.musiclibrary file you wish to open.

click here ➜ Use multiple libraries in Music on Mac - Apple Support

MrGabeT wrote:

I have already tried that, and it will still open in the external drive library.

Not possible. It would only do that, if you are selecting the library that's pointing to the external drive.

Make sure the library file you are selecting is the one pointing to the local media.

Unless of course, you have no other library, or your local library got merged somehow.

If there's only one file then you only have one library.

Or your local library file's media paths are pointing to the external drive, then it will look for media there.

Since you have not told us how you made this local library, it's hard to know what exactly is happening.