Transfer iTunes/Music Library from an old Intel Mac to a new M1 Mac with Ventura [If you have iTunes Match]

Maybe someone already explained this, but I only found similar situations described here and not this precise one.

I would like to share my case to help the community.

Many thanks to "Cristina", an Apple advisor that followed me in this process, step by step, with three calls to be sure each step was done in the right and best way.

Please note: I used Time Machine to move files, so this method can be applied only if you have an updated Time Machine backup of the "old" Mac.

Situation:

• I have old 2016 iMac always updated up to Big Sur.
• This Mac was born with iTunes, subsequently and recently updated to Music app.
• The iTunes library is 367 Gb, came from older Macs, but obviously the transfer between each computer was very simple because iTunes always "thought" in the same way, with the same folder structure.
• This library is synced with the cloud on all my devices thanks to iTunes Match subscription.
• This library contains both mp3 files obtained from my cds and purchased files (AAC, M4A)
• All Files has the id3 Tags, metadata and cover arts perfectly filled and, in many cases, adapted to my needs: eg., Pop gender may be divided in "Italian Pop", "Synth Pop", etc...

In this old iMac we can find two folders threads:

• iTunes, where all original downloaded or imported files are stored
• Music, where the old iTunes library has been converted in the new "Music Library" when iTunes changed (updated) to Music app.

The new Mac is a Mac Studio with M1 Max and OS Ventura 13.1.

Obviously it mounts Music App from the beginning.

• I opened Music App and logged in my iTunes account (therefore in my iTunes Match account too)
• On first attempt I tried to use the download option from the cloud (iTunes Match): this doesn't work perfectly for 2 reasons: first, original mp3, or other kind of audio files, are always converted in AAC when matching and uploaded to iTunes Match servers. This can be ok if you want to access them from other devices, you will download them in AAC (m4a) but if some reason you need to keep them as they was, be advised. Secondly cover arts will be damaged during the download: I'd say that more than 50% of 367 gb library will loose the cover art randomly (I'M REFERRING TO THE FILE YOU HAVE ON FINDER!) and will display the image only when you will play the song thru Music app. If you want to copy and use your original files in an other apps, such as Traktor, Rekordbox, Serato, they won't be displayed after the download.
• So I closed Music app, opened finder and renamed the library file in "Music Library Old"
• I opened the old iMac Time Machine with finder.
• I browsed up to the "Music Library" (not the iTunes one) file: I copied it KEEPING PRESSED "OPTION" to the same Music folder in the new Mac Studio, next to the renamed "Music Library Old" file.
• I deleted the first "Music Library Old" file
• I opened Music app: it started reading the recently copied "Music Library" file in background. In the lower left side of the Music app window you will see a message reporting the status of the library update. After 30/40 minutes it will finish.
• Now go to column browser and activate the "Download from the cloud" column: you will see an exclamation point. It means that you are on the right way, the library "remember" that original files were stored in a position and now can't find them. If you try to play them, a popup will appear telling the the original file / library can't be find. Close it and don't worry! See the next point

• Close Music App

Go to the Time Machine again, but this time browse in the iTunes folder, up to iTune Media / Music sub folder: this one should contain your original Mp3 / Wav / AAC files.

Click on this "Music" folder with audio file inside and KEEPING PRESSED "Option" copy it inside your new Mac's folder "Music / Media " (I try to translate, my Mac is in Italian language).

I have 367 GB of files, so in my case it it took some hrs to copy all, depending on the origin (Time Machine) and destination (Mac Studio SSD) disks, or depending on the connection tipe.

When it finished I opened Music app on the new Mac Studio, wait some minutes, and then started browsing or playing. All were fine, all feels are transferred, exclamation mark disappeared, etc...

I suggest to fo in "Album view" and with patience scroll all albums: you will see cover art in grey but after some time, they will load the cover art: it takes many time to the library to read again all.

RECAP:

You have to transfer 2 files only: Music Library file, and Music folder containing Audio files (Media), both keeping Option pressed, copying it from the Time Machine.

I hope this can help others avoid my anxieties. :)