hi there! thanks for posting this,
lets tackle the microsoft side of things. if u're using azure backup, check the backup policy settings https://docs.microsoft.com/en-us/azure/backup/backup-azure-backup-faq. sometimes migration resets permissions. make sure the backup service principal has 'contributor' rights on the storage account https://docs.microsoft.com/en-us/azure/role-based-access-control/overview. also, peek at the activity logs in azure portal, those logs love to spill the tea on what went wrong ))
oh and dont forget the classic, storage account firewall rules! migration might've flipped them on. here's how to whitelist the backup service https://docs.microsoft.com/en-us/azure/storage/common/storage-network-security.
if u're dealing with sql, run a quick 'checkdb' to rule out corruption https://docs.microsoft.com/en-us/sql/t-sql/database-console-commands/dbcc-checkdb-transact-sql. try a manual backup to a local path first, if that works, the issue is likely network or permissions. this might help in other tools too.
compare the old and new tenant's network security groups side by side. sometimes migration tools miss tiny but critical rules.
hope this gets u back on track,
rgds,
Alex