The features below are included in the September product update, deployed on 3 September, 2020.
Inbox "New Message" browser notification
When new messages are received, you will now see a badge icon (i.e. a small red dot) appear on the browser window tab. The red badge disappears when the Inbox page is loaded, and does not show if the Inbox page is already open when a new message comes in. Desktop notifications and audio alarms can also be enabled within your user profile settings if desired.
Browser tab badge:
Desktop notification (Mac version shown via Google Chrome):