At first, some people will be offended. "Why didn't you let me ping and buzz you and interrupt you all day? You didn't respond immediately each time :'((". Some people with unrealistic expectations may even stop talking to you entirely.
But eventually (years maybe) they will get overwhelmed too. No one can handle this madness indefinitely. I've seen giga-texters get broken down and turn into lazy texters like me, or at least learn to tolerate my long response intervals and recognize it as a coping mechanism rather than rudeness.
For important threads like calls or messages from important people/group chats, I have my watch vibrate.
Otherwise, I just go through my notifications once I have downtime.