A Humble email alternative app with a stop switch

Yes, it is a closed app like slack.

But you can request the sender's to contact you through Formal messenger by setting a permanent vacation responder in your email. Only humans read the automatic responder so your notification emails won't be affected.

For your machine communications like notification you can use email.

But for human communications you may consider Formal messenger because it organizes the incoming messages for you with help from sender's themselves.