Transferring music library from old MacBook Air (iOS 10.13.6) to new MacBook Air without iCloud

iCloud is neither required or used for music transfer like that.

See the following support document:

click here ➜ Move your iTunes library to a new computer - Apple Community

You can use a USB drive or other external storage to hold the library and and copy it onto the new Mac.

If your library is not consolidated, you will need to make it portable before it can be easily transferred.

click here ➜ Make a split library portable - Apple Community

Once the library has been copied over and is stored on the new Mac. Open the Apple Music app while holding the option key. It should prompt you to look for a library to open, navigate to wherever you placed the library and select the iTunesLibrary.itl file there so it can migrate it to the Music App.

I believe an iTunes library made in macOS 10.13.6 High Sierra won't transfer directly into Music. It needs to be updated in Mojave first. I have a small scale cottage industry (well over a hundred by now) of converting libraries remotely where Music doesn't like to play ball with .itl files. Monterey was particularly bad at it. If you send me your .itl file I can update it in the Mojave version of iTunes, then convert it using the Catalina version of Music, which should work in subsequent builds. Send the file as an attachment, or a link to it in iCloud Drive, Dropbox, OneDrive or similar. My email address is in my profile here. As Phil suggests it can help to have everything in the portable layout before you start, but there are ways around that or to repair things after the fact. I'll include advice when I return your library.

tt2