During the whole time I ran CEA (and now Forethought):
I never had Slack or work email on my phone.
About 4 times a year, I took week-long holidays where I wouldn’t check Slack/email (but where people could WhatsApp/phone if there was anything urgent, which they did on average ~1 times/week).
After I left CEA, I also started trying to take ~20m breaks every two hours, to meditate or read, and let my brain recover from intense work. (Maybe I should do this again?)
I’ve done this for 10 years, and though these organisations are pretty large, I don’t think this has ever caused major problems.
Some benefits of this:
Rest is good for your work: you will have more energy the next day, and you might come back with a new perspective on an important problem.
You’re not missing out: I think most things will not be urgent to respond to in less than 12 hours or whatever. You can ask people to call you if something actually urgent comes up.
You’re modelling behaviour that’s more likely to be sustainable for your team, empowering them to take their rest seriously as well.
Almost no-one needs to check Slack or email when they’re not at work. Moreover, I think that checking Slack outside of hours hurts your rest for little benefit.
I recommend:
Not having Slack or work email on your phone (or personal computer).
Telling your colleagues to send you a text/WhatsApp if you’re needed urgently.
The same applies to holidays: don’t check Slack/email, tell your colleagues to message you if there’s something important and urgent, and relax.