How do I change my Apple ID region without losing my entire Music library or lose access to iCloud storage?

Hello, I have recently moved to NZ and I need to change the region that my Apple account is registered to.

When I have tried, I get a warning message saying I will lose my entire Apple Music library and will need to re-download it again once I have changed regions. Is there any way I can back up my library before I delete it in order to change regions, then re-download the previous library once the regions have changed?

Separately, I also pay a monthly subscription for additional iCloud storage. I am worried that if I proceed with changing regions on my Apple ID, it will affect the files/photos/etc I have saved on iCloud.

Lastly, I am part of a family group and share my Apple Music and iCloud with my family. How will the changes in region affect the other individuals that share the music and storage?

Any help would be greatly appreciated!