Email account for apple id has been hacked. How can change without losing all my backed up data, music

It shouldn't affect it at all if you change your ID to the new one.

Change information in Apple ID - https://appleid.apple.com/

Change your Apple ID - "Follow these steps to change the email address that you use as your Apple ID." Plus special instructions if your Apple ID ends with @icloud.com, @me.com, or @mac.com

https://support.apple.com/HT202667

and

What to do after [or before] you change your Apple ID email address or password - https://support.apple.com/HT204071

"After you change your Apple ID email address or password, you might need to update your sign-in information with any Apple services you're using." - Or if you're seeing persistent disabled messages or repeated requests for the password to your previous AppleID.

See the instructions in Change your Apple ID - Apple Support

and be sure to note the following from that link:

Before you change your Apple ID email address, you need to sign out of every Apple service and device that

uses your Apple ID. If you want to use your iPhone, iPad, or iPod touch

to change your Apple ID, stay signed in to your Apple ID on just that

device.

My Apple ID is used to sign into several areas of "iCloud" all separately on my phone. I have to do it for iMessages, then again for the App Store, and presumably also for the iTunes Store (which I have never used) and I think yet again for iCloud Drive. So if I were to change my Apple ID I would have to sign out of there.

Your email address is your Apple ID. If you are going to continue to use your same email address now that the hacking issue has been resolved then you don't need to do anything. If you have changed your email address then you have changed your Apple ID for that account and everything will be intact in the account and you may only need to sign out and sign in again on the various services so they are now using your new ID. It's a little bit like changing your name. If you change your last name you need to notify your bank and your gas company and your electric company about your new name, but your house is still the same. When my wife got married she changed her name, so she told the bank and they changed the name on her account, but it remained the same account and her money was all still there. She then had to tell the gas company, etc. about her name change so they would know to bill that account with the new name.

You don't lose anything if you follow the procedure in Change your Apple ID - Apple Support

It just changes the address that is used for your ID.

Yes, just change the email address in the information area for the existing ID. Do not set up a new Apple ID account.