Moving music library from old MacBook Air (2017) to new one (2025)

I'm trying to move my music library from an old MacBook Air (2017, Monterey OS) to a newly purchased one (2025, Sequoia 15.5 OS), but have been only partially successful.

I have copied the iTunes folder from the Music folder on the old machine to the Music folder on the new one via Airdrop. And when I open Apple Music, all my albums/songs/playlists match up with what's on my old machine and can be played successfully. However, artwork has appeared on only a fraction of the titles; the vast majority are blank. On the old machine, ALL my songs/albums have artwork successfully attached.

I've seen some advice online that says I need to open Apple Music while holding down the Option key, which prompts me to choose a library file (iTunes Library.itl) to link to. I have tried this, but this doesn't seem to have made any difference - and worryingly, the only library file I can see is dated 2019. Surely there should be a more up-to-date one than this?

In case it's relevant, I'm not a current Apple Music subscriber; most of my music collection is ripped from CDs, and the rest is iTunes downloads. I also haven't yet de-authorised the old machine, in case I need to copy the Music/iTunes folder again. Plus, I seem to have a lot of old, out-of-date files in the old Music/iTunes folders, which may be causing an issue.

Any advice as to where I might be going wrong would be hugely appreciated.