Thanks RobertCrick1. Just to confirm that this works but only for multiple messages. To recap for people having this issue in new Outlook (as of Sep 24, 2023), read/unread status will sync with Gmail only if you select more than one message. To replicate the issue on a PC:
- Open New Outlook, and open Gmail in Chrome.
- View a couple or more Gmail messages in the New Outlook. They will become read in Outlook but when you check Gmail in Chrome, they are still unread.
- Go back to Outlook, and select those same messages that did not sync. (You are selecting multiple messages by clicking the radio button on the left of the message heading in the message list pane. The radio button shows up when you hover the mouse over the sender's initials).
- Right-click on one of the selected message for the menu, click to 'Mark as unread' first, then click to 'Mark as read'. (This action will apply to all the messages selected).
- Go to Gmail in Chrome and those messages will now be marked as read.
- Note that only the action to 'Mark as read/unread' works when selected from the right-click menu. It does not work when you select multiple messages and change their status by clicking the envelope icons on those selected messages.
So it looks like the new Outlook is actually able to sync read/unread status with Gmail, which means that some aspect of the IMAP protocol works, but only when multiple messages are selected and when the status is changed only through the right-click menu.
Does it even need to be said that this is embarrassing for Microsoft. This level of inconsistency of programming in a major app for email is below the level of a mediocre computer science student. Even if this issue has to do with something on Gmail's end, the Outlook programmers should have figured it out.