where is my music stored? Is it backed up?

If you have set Time Machine to backup your hard drive, then it includes the Music folder which should hold your iTunes / Music library.

You can of course back it up independently from the Music folder in your User profile folder.

See here: link -> Change where your music files are stored on Mac - Apple Support

Music is backed up to iCloud, if you’re using Apple Music, or iTunes Match service.

Use iCloud Music Library on PC - Apple Support

Music stored locally is backed up in Time Machine.

How to back up your Mac - Official Apple Support

Here’s a description of how to create an additional backup:

https://www.imore.com/how-back-your-itunes-library

Here’s how to back up the contents of iCloud:

Archive or make copies of the information you store in iCloud - Apple Support

And since you mention iTunes, and have a new Mac arriving:

What happened to iTunes? - Apple Support

When you buy a new Mac the easiest, quickest and most reliable method is to simply connect the old Mac's Time Machine External Hard Disk to the new Mac using a USB cable before you turn on the new Mac. When you start the new Mac for the first time it will startup Setup Assistant (SA), SA will get to a point where it asks if you are migrating from another computer, select Yes  and follow the on-screen prompts and it's done! It is THAT simple.

If you have already done SA on the new computer then simply connect the Time Machine External Hard Disk using a USB cable and launch Migration Assistant (MA) which is located in Applications - Utilities - MA. Then follow the on-screen prompts.

The ONLY difference between MA and SA is MA will create a new user account that you need to log into.

 Both SA and MA migrate applications (not 32 bit apps) , data files, settings, it does not migrate Mac OS itself. Some professional apps such as Adobe and Microsoft apps may require re-installing their apps as they will not allow them to be migrated. As long as you kept the security keys for installing their apps, it is not a big deal.