The way I deal with it is not responding immediately other than by accident. People stop expecting it when you stop doing that. They adapt. And they appreciate when you eventually do respond. Basically asynchronous communication makes responding more efficient. Instead of constantly attention hopping you simply periodically respond to stuff in order of priority. When urgent stuff really needs attention, people will find you.
I turn off notifications/alerts for most things and I simply check when I have some time. Tools and apps begging for attention rank very low on my priority queue of things that need attention. Most email I still receive is actually notifications and not requests for lengthy replies. I rarely use email for discussions of any kind any more. Wrong medium for it. If my phone rings, it's generally a spam call. Most important calls are scheduled. And I prefer taking them on my laptop via a video call. If I don't recognize the number, I don't answer at all.
All this eliminates interruptions of rare moments I have when I can actually focus on something. Focus time is actually blocked in my calendar and I don't allow stuff to creep into that other than by exception. And I strongly encourage people to not even attempt to book meetings with me outside a few dedicated slots I have for that. There's always more stuff to do than I can do. So, it's important to cherry pick and do it well.