I have an iPhone 12 and an Apple Watch SE2 and most of the time, I don't recieve notifications on my watch for my Messages app, no matter if it is regular SMS/MMS or is iMessage. Other notification works and sometimes Messages come through. I've reset the watch and the phone several times and it didn't solve the problem.
Note that I have a couple contact lists and some contacts are on both lists. That doesn't matter, because that's not the only contacts that have problems....