Update: This is now resolved. Here the issue was the DB was about 30gb but limit is 4.
As documented here: https://learn.microsoft.com/en-us/azure/app-service/manage-backup#configure-partial-backups
After removing the database from the backup, the app service backed up as expected.
Helpful document links:
SQL Automatic Backups: https://learn.microsoft.com/en-us/azure/azure-sql/database/automated-backups-overview?tabs=single-database