migrating itunes from an imac to a macbook

See Move your iTunes/Music library to a new computer - Apple Community. In general if you copy everything across exactly as it was, into an identically named user profile, it is going to work. It will also work if the library is in a portable shape and you move it to a new location. It gets complicated when neither condition is met. You can either revisit the migration, or see if this post helps you: Locate multiple missing songs - Music - M… - Apple Community. If you post back the three details I ask for there I may be able to suggest a simple remedy, if one is available.

tt2

See Managing your Mac media libraries - Apple Community for some background on the standard layout of a Music library. Having this layout where the library file is inside <Some Path>/Music and the music is all within <Some Path>/Music/Media should yield a portable library that can work correctly when the Music folder is moved to <Another Path>, which might be on another drive. Specifically moving the media folder via Finder and then updating the music media folder location may sometimes work, or Music may be able to automatically repair things when it doesn't, but it isn't the correct way to do it. The second link in first post details a tool I built to help when Music can't fix things by itself. Far better to move the library sympathetically in the first place if you can. This may be possible if you can massage the media to the right location on the current source drive, where the Mac's file system may be able to correctly locate files moved around on the same volume.

Otherwise you should use the Consolidate Files tool to copy the files from their current location to a new media folder on the external drive. I'd suggest copying the current .musiclibrary database into <External>/Music first, using the option-start-Music method to connect to the library on this new path, then setting the media folder to <External>/Music/Media and finally using File > Library > Organize Library > Consolidate Files to copy in the tracks. At the end of the process the external drive can then be connected to any Mac running the same or a newer version of Music and it can open the library, updating it if necessary. Once it has been updated to run on a new version of macOS you won't be able to take it back to the original machine without downgrading the library. (I.e. restoring or connecting to the pre-upgrade version.)

tt2