Hi! Sorry to hear that you have trouble with this situation. When you add the email in some email handler apps, even after you close the session on all devices, it could remain open. Please review that you have followed all these options.
First, please check your draft, as the attacker could have scheduled these emails to be sent later. If that's the case, in your draft emails, you will see a "scheduled" legend next to the emails.
Also, you should check that your contact methods remain the same here:
https://account.live.com/proofs/manage/additional
After that, close all your open sessions. You will need to log back in to all your devices, but it's safer this way:
https://account.live.com/proofs/manage/additional
After this, please review the next link to see if any apps that you don’t know have access to your account and delete them. This is important:
Finally, do this in Outlook from Edge:
Sign in to Outlook.com
Click on the gear icon (Settings) in the upper right corner.
Look for and open Mail settings.
Go to the Rules section and check if there are any rules you didn’t create. If there are any suspicious rules (for example: “forward everything to @.___” or “move everything to Deleted”), delete them immediately.
Also, check in Forwarding and IMAP again and make sure there are no addresses added. If there is one and it’s not yours, remove the forwarding.