Adding email as a left tab panel remains under review. We are working on adding several Teams and email integrations:
- Share to Teams: Share a copy of an email and any attachments into a chat or channel directly from Outlook
- Share to Outlook: Share a copy of a channel or chat conversation via email directly from Teams
- Actionable Teams Activity Emails: Teams missed activity emails display the latest replies and allow you to reply directly from Outlook
See this post for more information:
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My suggestion is similar, but to replace the current 'X' which dismisses the notification dialog, to have two interactive text buttons. One which reads "Mark as Read" and the other would read "Dismiss".
Mark as Read would both dismiss the notification and mark that conversation as read in the Teams client. Dismiss would just dismiss the notification as the X currently does. Leaving the notification in Teams that their is an unread chat.