Using Outlook for iOS for personal email and calendar management
Since mail arrives fine on your iPad and phone, your account itself is working, so this is a sync problem in the desktop app only.
First, force a manual sync. In the new Outlook desktop app, open Settings and review the sync settings for the account, including how far back mail is set to sync. In classic Outlook, use the Send/Receive tab and choose Update Folder.
Next, check the inbox view is not hiding mail. Make sure the filter is set to All rather than Unread, and check the Other tab if you use Focused Inbox.
If it still stalls, remove the account from the desktop app and add it again. This rebuilds the local mail cache and usually clears a stuck sync.