how to import the entire music library into another computer

This should be a simple question, however I've search for days online and I cannot find an answer to this.

I have an iMac and a Macbook pro. I have the Music APP (formerly iTunes) installed on both. I have moved the songs manually from the iMac to the laptop using an external drive. I have exported the library also to that drive. However, I cannot find the option to IMPORT that library into my laptop's Music App. I'm hoping that some more experienced people can help me out.

Apple did (yet another) stupid move calling the old iTunes Apple Music App, only to create more confusion with the Apple Music online service. Well done Apple! Because of that I want to clarify:

1) I need to copy the Apple Music APP's library, not Apple music PAID service.

2) I have Apple Music APP not iTunes

3) I don't want to use iCloud to sync it

I want to copy the library file from my iMac (OS Catalina) to my laptop (OS Sequoia)

Thank you in advance nice people.