Neither Tableau Server nor Tableau Online won't triger any email about new dashboard available in Server.
There is a subscription option but it wont serves the purpose since it will be helpful only to receive the timely updates.
If you want to send email to every user when you send a dashboard then you need to integrate the Postgres DB of Tableau Server with ETL/Python/R/.net/Java.
To check for the new row in workbooks table of tableau server postgres DB and use any one of the tool mentioned above to send a mail to group of users below are the tables
hist_workbooks Records the most useful information about a workbook that was relevant at the time of the event (see workbooks table). workbooks Each record represents a workbook that exists on the server.
Useful links to access tableau server DB:
To send a email from Python:
Hope this helps
Plz mark this answer as correct & helpful to close the thread
Tableau announced webhooks at the Tableau Conference which will probably allow you to alert people when a new version of a dashboard has been published, but it is not available yet, and also not in the beta/pre-release program.
Johan de Groot