While we don't currently have this functionality in the product directly, but you could potentially use Microsoft Flow or some other service to send a note when a new comment is entered into the table in the catalog database.
This is something we're considering for a future release, but don't have a specific timeline when we'd be able to go ahead with that work at this time.
During testing, I noticed that when a comment is deleted from the Report Server, it is also deleted from the Comments database table. Is this going to change so that all comments are left within the table (with a flag that shows as deleted), even though no longer visible on the Report Server?
Do we have the feature enabled in the Power Bi Report Server where a business user can use '@ username' and a notification is sent to the 'user' regarding the same?
I see this features availabl in Power Bi Cloud services, but since our company is still using PBIRS, we still have to sent emails for any comments on the reports/dashboards, which become confusing over time when there are multiple questions/responses.