I solved this issue by never unmuting my phone. Not even for phone calls (unless im expecting an important call). My phone doesn't tell me when to use it. I do it the other way around. I check my phone maybe 2-3 times a day. When I wake up. Once a little after lunch. And once at night.
The main thing you have to do is not feel like its your job to immediatly attend to any contact. Treat your phone like a laptop. Emails you should reapond to in 24 hours. Text or phone calls don't need to be answered. Your phone saves your call logs for your convenience. Just get back to that person when you have a free chance. Our ancestors survived not being able to talk to any one at any moment. We don't have to either.