This topic addresses a similar issue, but not this particular one.
I’d like to disable “your post was approved” emails for users. Currently we have a) approval needed for all posts (we’re fairly small) and b) emails on for all watched topics. I don’t see a setting that controls other email notifications.
I just tested this with a dummy user and received an email notification if the post was approved after I had logged off the dummy account AND while currently still logged in (I also saw a notification in the notification centre).