(Full story: https://github.com/OfficeDev/office-js/issues/2358)
Back in Office add-ins Community call March 09, 2021, Microsoft revealed that admin-deployed add-ins would be automatically pinned to the ribbon in Web Outlook starting 21 April, 2021.
We have many customers who already had deployed our add-in via Centralized Deployment before that date, but would now like to have it auto-pinned in Web Outlook.
However, in our internal testing and testing done by our customers, re-deployed (remove+add) add-ins are not automatically pinned in Web Outlook. In addition to lack of auto-pinning, we are naturally not seeing the "nudge" notification.
Completely new add-ins (not previously centrally deployed) are properly auto-pinned.
I suspect the issue is in the design - the auto-pin was probably designed to increase the visibility of completely new add-ins, hence the nudge notification. But the auto-pinning is needed also for previously deployed add-ins. Centralized Deployment probably remembers the add-in was previously deployed (because of the same App ID) so neither auto-pinning nor nudge notification are triggered.
Add-ins deployed via Centralized Deployment before April 21, 2021 should be auto-pinned in Web Outlook when they are re-deployed or updated. They don't need to have the nudge notification (unless you can track whether the user has ever used the add-in).