Assuming that the error complains about Mailbox Quota exceeded, yes, this means you reached the allocated space for the cloud mailbox (example 50gb/ 100gb). You can check Get-MailboxStatistics and Get-MailboxFolderStatistics | ft foldersize, targetquota,folderpath in EXO powershell. I am on my phone so apologies if I have typos in the cmdlets. Solution would be to reduce the size of the mailbox (start with deleting junk or duplicate data) or depending on the mailbox plan assigned, you can increase quota up to 100gb or have an archive mailbox to the primary mailbox. If you have migrated from Gmail, you might have duplicate data in the Archive folder (which would be equivalent of All Mail in Gmail).