Help with watch only notifications while wearing.

Hey all, I switched to iPhone a little over a year ago, and just moved to the Apple Watch 6. I thought this feature was default and it is not, and here is a problem I'm trying to solve.

I have Emergency Bypass on for a number that I must answer for work. I was told that when wearing the Apple Watch, it would send notifications there, even when sound was on for the phone. And Emergency Bypass ALWAYS has sound.

The problem I'm trying to solve is I want the emergency bypass for overnights, but during meetings or church, I don't want audible alerts. I don't want to have to remember to silence my phone, because I'm in fear of forgetting to remove silence overnight, LOL.

I'm looking for a solution that allows a number to ring on my phone when I'm not wearing the watch, but go to the watch in vibrate when wearing it, so emergency calls don't BLARE during meetings, etc.

Ideas? Thank you for any ideas!