On my phone I can set certain contacts to have priority over do not disturb so a message or call from that contact will still come through. Last night I missed an important message from my wife and noticed when I had first went to bed but hadn't fallen asleep yet none of my notifications were coming through on my watch but after I got up this morning the watch was sending notifications fine. My guess is that it was not notifying because I was within my sleep window (looking at the details this morning). I hadn't put my phone on DND yet and would hear the notification there but not on my watch.
So is there a way to set certain contacts to a priority so they will still notify no matter what?