I don't understand. Why would you have to have a github tab open and refresh? There have always been email notifications for all these events. Also, why is getting these notifications in chat preferred over email?
Emails are in their own isolated packages. If i get an email saying the build broke, there is no easy way to check the last time it happened. I wouldn't be able to glance at the last few messages and see that the build breaks every time "X" commits or the tests fail every monday. I can't easily get context on what someone was doing when it broke.
With something like slack it's all right there. The last 3 alerts, maybe a few messages from devs quickly explaining what happened (or preemptively saying that the build is going to break, and it's okay), someone taking responsibility and saying that they will handle the fix, etc...
I would just create a folder and a mail rule that moves the mail automatically. You would actually be able to filter your mail with more granularity than what a simple Slack channel can provide
When the notification comes into Slack that the build broke, I can immediately type in the chat "I'm looking into that one" and everyone knows what I'm referring to and knows instantly that they don't need to waste time on it.
At my workplace, everyone is usually always active in chat working out problems and having discussions, so a notification is more likely to be seen by more people sooner in the chat than in an email.