Hello IT Admin,
Welcome to Microsoft Q&A Forum, thank you for posting your query here!
Since the restore point is mounted as read-only, you cannot change a mounted point to read-write.
Instead, you can manually copy the files to a different writable location (such as another volume, file share, or local disk). Then use the Instant Restore feature to mount a writeable recovery point snapshot as a recovery volume. You can then explore the recovery volume and copy files to a local computer.
You can refer to the below MS Article for better understanding:
https://learn.microsoft.com/en-us/azure/backup/backup-azure-restore-windows-server
And as you mentioned, if your primary server got down/lost where the backups were taken, you can restore the backed-up data to an alternate machine (in New Domain) by using the same passphrase that you provided during registration.
Here is the necessary steps to follow this method: https://learn.microsoft.com/en-us/azure/backup/backup-azure-restore-windows-server#use-instant-restore-to-restore-data-to-an-alternate-machine
in this way you can restore the data to the new domain.
Hope this helps!
Please reply if you have any further queries.
Thanks