Sending, receiving, and organizing email in Outlook.com
Hi,
Are the missing emails from specific senders?
This usually means your mailbox filters moved them, so check Rules, Junk Email, and Blocked Senders, then search your inbox using the sender’s address to see if the emails went to another folder, also check Focused and Other tabs if enabled, and sign out then sign back in to refresh sync.
Since your test email sent fine, the service is working and this points to filtering or mailbox settings.