I have never worked in an environment like this. I'm sure there are jobs where you do not need to be always on slack.

My work used to be like this too, except Slack didn't exist yet so people used phones to call you. When I explained the problem to my boss, he told me not to answer the phone and set it to silent. Now most of the company use mail for uninterrupted messaging and everything runs much smoother and less bugs because I could concentrate on the job.