Not OP, but it's good to turn them off for sessions of focus. They can, almost always, wait.

I have my notifications for Slack and Outlook turned off. I get a Dock tile badge, and Slack does ping my wrist via smartwatch, but not much else. Most emails I get are not vitally important, nor do most of the things I get on Slack immediately required reading or actionable.

Notifications need to be off if you’re doing focused work, and good managers will not only know this, but support you in it, or even expect you to set this boundary in order to do your best work.

Simplest version is to have agreed upon avenues of escalation, which can be ”if someone doesn’t respond in the timeframe you need, pick up the phone and call them, and if they still don’t respond, pick up the phone and call their boss”.

Then from your end, you just need to make sure your boss is set as a favorite contact or whatever is required for them to be allowed through your do-not-disturb settings.

You can also set other routines like weekly check in meetings with certain groups. Often times people don’t need you right now, but they think blowing you up on slack is the only way to get what they need. By setting aside a couple hours one morning and having several “office hours” style meetings, you give people the comfort of knowing they have a time they can get your attention, and that often cuts down on 50-80% of the ad-hoc interruptions.

Process The Comms Async.

Async doesn't mean "rarely", it means you must set the pace. Notifications contradict this paradigm, so they are completely off.

I switch to these tabs/apps manually, at my own pace, which is sometimes relaxed, but at times can be super-dense.