I have (3) gmail.com accounts in the new Outlook. At times, it shows new emails for one or more of the accounts. However, when I look at them, they were read a week or so ago.
However, it is better than the old Desktop Outlook. Frequently, it did not alert me of unread messages when there were some. MS support was never able to fix the old version.
Update: I found out, when a false new item shows up. I go to Gmail and mark it as read. Then it stays as read in Outlook. Do I guess when reading a message, at rare times, it does not update the Gmail server.
