Why is the email notification “We encountered an issue while backing up these mailboxes caused by not enough space on the mail-server side” sent?

When our system finds the Microsoft API Error “ErrorQuotaExceeded” during the backup process, it triggers the email notification. To fix the backup error, please ask the organization to free up some space or add more space in the mailbox, which would eventually remove the Microsoft API Error. Once action is taken, the Backup process will automatically resume.