Unable to fully restore ITune/Music database from 2019 16" Intel Macbook Pro on Big Sur to 2023 M2 14" Macbook Pro on Ventura

the fully speced 2019 16" Intel Mackbook I got a few years ago turns out to be a flop as it has serious heating issues. I have tried going to Apple Care, but they haven't done much to improve it. I must use the laptop with very cool air-conditioner, but still it would suffer from overheating. So I was forced to buy the M2.

I am a DJ, and I need to restore the ITune database in its full directory structure which is stored on an external harddrive on the M2 exactly as it was, so that my DJ software Rekordbox can maintain the analysis and playlist derived from the ITunes database directory.

However, I cannot resotre the full data base on the M2. I can open the ITunes. ITL file , but the restoration only works for a small fraction of the music. A large portion of the music is not shown in ITunes on the M2...

Any tips or workaround would be much appreciated!!!