Q: backup with new ID

Apps/media/other downloads are forever tied to the AppleID used

to download them. You cannot transfer items from one AppleID to

another nor merge AppleIDs.

If you wish to use only the new AppleID, you will have to download everything

you want using the new AppleID. Items that were previously purchased using

the old AppleID will have to be re-purchased using the new AppleID.

You may wish to look into Family Sharing (Set up Family Sharing - Apple Support)

to see if this would give you some of what you want.

You can also change the email associated with an old AppleID rather than start

an entirely new AppleID.

Change your Apple ID - Apple Support

https://appleid.apple.com/