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this was definitely the problem. Added more info.
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This might bewas the problem. It's not me, it'sIt wasn't me; it was them.

  Microsoft said the following here: https://portal.office.com/servicestatus

Update: Since then, all the test emails I had sent to myself, which weren't delivered, have been delivered, so it seems like Hotmail/Outlook is working again.

Title: Emails aren't delivered to recipients User Impact: Users can send email but the messages aren't being delivered to the recipient. Current status: We've developed and successfully tested a fix that will address the issue. We're now in the process of applying the fix to restore email delivery. Start time: Saturday, October 3, 2020, at 7:00 PM UTC Next update by: Sunday, October 4, 2020, at 10:00 PM UTC 

enter image description here

This might be the problem. It's not me, it's them.

 https://portal.office.com/servicestatus

enter image description here

This was the problem. It wasn't me; it was them. Microsoft said the following here: https://portal.office.com/servicestatus

Update: Since then, all the test emails I had sent to myself, which weren't delivered, have been delivered, so it seems like Hotmail/Outlook is working again.

Title: Emails aren't delivered to recipients User Impact: Users can send email but the messages aren't being delivered to the recipient. Current status: We've developed and successfully tested a fix that will address the issue. We're now in the process of applying the fix to restore email delivery. Start time: Saturday, October 3, 2020, at 7:00 PM UTC Next update by: Sunday, October 4, 2020, at 10:00 PM UTC 

enter image description here

Source Link

This might be the problem. It's not me, it's them.

https://portal.office.com/servicestatus

enter image description here