The title says it all—this is yet another regression with the unannounced, untested, unwanted launch of the redesigned top navigation bar. Moderators have a diamond icon in their top bar, which is ordinarily the same color as the other icons (inbox, achievements, etc.), but is supposed to light up in a different color when an "interesting" event occurs. In Stack Overflow's color scheme (I'm not sure if all sites were the same), it turned blue when there were new (unread) messages in the moderator inbox, and it turned orange when there was a notification pushed to us by staff. This is no longer working; the moderator diamond remains dark-gray (or white, depending on your chosen theme) and does not change colors when new inbox messages arrive.
I am assuming that this behavior reproduces on all Stack Exchange sites, since they share the same top bar, but, of course, as I only have moderator privileges on Stack Overflow, I can personally only reproduce it there (and on Meta Stack Overflow). I've confirmed the regression after disabling all userscripts, and I've double-confirmed with other Stack Overflow moderators that they are seeing the same regression.
Of note is that the page still knows new notification(s) have arrived: the tooltip text changes from "Moderator inbox" to "New items in the moderator inbox". In addition, a style class is present on the link element in the HTML that is supposed to set the foreground color (e.g.,
fc-theme-secondary-color). Unfortunately, there does not appear to be any matching class defined in the CSS.
Due to this regression, I missed several dozen notifications. This makes it difficult for moderators to do their job. Please revert to the working version until you get all the bugs worked out. Thanks!