Hi, I understand why this feels like a hack, but this issue is usually caused by account sync or mailbox status not updating. Are you seeing this in the web version of Outlook or only in the app?
If your inbox shows full even after deleting emails, the mailbox status may not have refreshed.
Sign in to Outlook on the web, then sign out of all sessions from your account security page, and sign back in on one device first.
This forces the mailbox to resync and update its storage status.
If you use the Outlook app, remove the account and add it back after doing this. Also check your recent activity page for any unknown sign-ins. If there are none, this is not a hack but a sync issue blocking sending.