Sending, receiving, and organizing email in Outlook.com
Sorry to hear about this issue. First, confirm whether you can send emails and whether the same issue occurs both on Outlook.com and in the Outlook app.
If it's the app, please sign in directly at Outlook.com using a private or incognito browser window and check whether the missing messages appear there. Also check the Junk Email, Other, Deleted Items, and Archive folders, and make sure the message list is sorted by date.
Next, go to Settings > General > Storage and confirm that neither your mailbox nor your Microsoft cloud storage is full. Then check Settings > Mail > Rules, Forwarding, and Junk email for any setting that could be moving, forwarding, or blocking incoming messages.
Please send a test message to the account from a different email address and let me know whether the sender receives a delivery-failure message.