See Move your iTunes library to a new computer - Apple Community for general background on moving the library and migrating to Apple Music. I should work much the same as iTunes as far as music is concerned. There are changes for audiobooks, podcasts, and video content.
That said I've seen a number of posts lately where Monterey fails to correctly convert an iTunes Library.itl database correctly and just sits there with a spinning busy icon. There seem to be two possible workarounds, copy the .itl file to Big Sur or Catalina and convert it there (the media folder is not required) then move the database to Monterey and place it above the media folder, or if you have an iTunes Library.xml file you can import that into an empty Music library with File > Library > Import Playlist... as long as the media files are at the paths listed in the XML file. This method loses date added details.
If you don't have the XML file or access to Catalina or Big Sur I could convert the library for you. I've done several over the last week or so. You can send me the .itl, or a link to it on a cloud service such as iCloud Drive, OneDrive, Dropbox, etc. I would convert the library to the .musiclibrary format and post it back to you. You'll find my email address in my profile here.
tt2