There is literally no way anyone can interrupt me when I'm working, unless they are already in my house.
Again, tools can help modulate the above behavior and even build norms. But ultimately, they only work if everyone agrees to the same set of social norms.
For example, if you feel you need to respond to any DM (either implicitly due to company culture or explicitly because your boss has brought it up as a complaint about you), then slack is a huge interruption. You probably feel the need to have intrusive notifications enabled and/or a bouncing dock icon indicating new messages.
On the other hand, if the norm at your company is "slack is async so expect a response in 2-3 business hours," then yeah - it's rarely, if ever, interrupting.
A Faraday cage may become an important component to taking time for relaxing.
One thing that's easy to forget is that technology does not solve political / social problems. The big problem is that far too many people think they can run around and interrupt people at any time for any reason, and no piece of technology will solve this. If you send them to a tool that breaks their ability to interrupt, then they will figure out a way to bypass the tool.
I think it's more important to advocate publicly to be conscious of how we interrupt each other. It's very important that interrupters recognize their behavior.