Apple Music

Starting with Catalina, iTunes (on the Mac) became Music. The main difference is that you now sync your iPhone with the Mac using a Finder window rather than iTunes.

Use the Finder to sync your iPhone, iPad, or iPod with your computer - Apple Support

Other than that nuance, Music is pretty much iTunes.

Syncing is designed to sync from the computer not the iPhone, not the other way around. Perhaps these articles will help;

Move your iTunes library to a new computer - Apple Community

See also How to move your iTunes library to a new computer - Apple Support for Apple's approach to this topic.

The steps given below should help if your iTunes library is empty or missing content:

Empty/corrupt iTunes library after upgrad… - Apple Community

kathrynfromchalfont wrote:

How can I import music from my old iPhone 5 to my new MacBook Air? Do I need a program ?

Yes, you need a third party program. The native iTunes and Music apps do not provide a way to move non-purchased content from the device to the computer. If you want to give it a try, check out this user tip by turingtest2: Recover your iTunes library from your iPo… - Apple Community