People managed to deal with that for thousands of years without carrying phones with them everywhere they go.
For those thousands of years, your boss or clients didn’t expect you to always be available.
That said, it’s not an excuse. Put your phone on silent when you pay a shiva visit, and don’t check your messages until you leave. No boss or client has a right to make you such a slave that you can’t be unavailable for 15 minutes. It’s more about self control than it is about a real need to be perpetually accessible.