Using older versions of Outlook for Mac for personal email and calendar
Please first sign in to Gmail.com and confirm that the new messages appear there. If they do, the problem is with Outlook’s local synchronization rather than Gmail delivery. Remove and add the Gmail account again through Outlook > Settings > Accounts > Add Email Account, completing the Google sign-in and selecting Allow when Google asks whether Outlook may access the mailbox.
Let me know if this works or if you have trouble adding it back, please.