Keep the phone on silent enable notifications on the watch. You get to keep an eye out for anything important while being away from the phone takes a bit of effort to reply immediately.
Im using an older garmin watch and it works perfectly, it even has a silent zone setting so I never get disturbed when I sleep. Also has a really neat feature where I can ask the watch to ping my phone if I cant find it, so when I get an important message and I need to find the phone I could quickly find it.