Managing personal Outlook.com account settings, security, and privacy
There actually is a way to reach a human for a personal Microsoft account, although Microsoft unfortunately makes the route less obvious than it should be.
For a personal account, Microsoft currently recommends using the Get Help app. After signing in with the affected Microsoft account, describe the problem and run through the suggested troubleshooting. If the automated troubleshooting does not resolve it, the app can present a Contact Support option, with available contact methods potentially including chat with a support agent or a callback. The options shown depend on the product, issue and support hours.
Microsoft Support: Get Help for personal accounts
There is also an important detail about your email problem: if your Outlook.com mailbox was actually over its storage quota when those messages were sent, Microsoft states that those incoming messages are returned to the sender. They do not sit in a queue waiting for your mailbox to become available. Once you are back under the quota, the senders will need to resend those messages.
Before contacting support, I would also check Settings → Storage rather than relying only on the amount of space shown elsewhere. Microsoft notes that Deleted Items still counts toward the mailbox quota until it is permanently deleted.
If your storage page shows that you are definitely below the limit but Outlook.com is still refusing new mail, then I would contact support and describe it specifically as:
“My Outlook.com mailbox exceeded its storage quota. I have permanently deleted enough email to bring the mailbox below the quota, but Outlook.com is still not accepting incoming mail. Please check whether my mailbox/account is still flagged as over quota.”
That gives the support agent something much more specific to investigate than simply saying that email is not syncing.