This .tl library import function is broken in Monterey. If you're able to upgrade to Ventura on the new machine that doesn't suffer from the same issue and should upgrade .itl files correctly. Alternatively the .itl files can be converted using Catalina or Big Sur. The media files are not required to be present for the conversion. I've done a bunch of these remotely with people sending me their .itl files, or a link to them in a cloud location, by email, and me posting back a link to the converted .musiclibrary database in my OneDrive folder. Should you need me to do this for you then you can find my email address in my profile.
tt2