Using New Outlook on Windows for professional communication and productivity
The Outlook Team did some work in late December to address this issue. I am not sure the fix build though. I just tested this with my version at work with my Gmail account and I was able to see it working properly. I did read/unread in New Outlook and it showed up on Gmail web ~10-20 seconds later.
In New Outlook if I go to Help, Diagnostics, my version shows as: Client Version: 20240112004.07.
If you are at this version or higher and still repro it would probably be worth submitting an In App ticket (Help, Support).