I am also experiencing this. This has been an intermittent issue for about a year for me. I miss message all the time because the phone doesn’t make a sound, because I’m assuming, it thinks the Watch is notifying me. I get no dot, no haptic, no sound.
But just as frustrating, it does this on the phone too if I’m not wearing my watch. It delivers silently. No sound (unless I physically have the phone unlocked doing something), no haptic: but I do get the badge on the app.
My settings are all correct on phone and the Watch. I have (another) call with Apple Support tomorrow to try and resolve, but it’s not the first time this has happened, and won’t be the first time they can’t resolve the issue if we don’t tomorrow.
All my other notifications work as they should: emails, WhatsApp, Sleep, Health, music etc etc. But Messages? Nope.
I’m beyond frustrated with it as it’s been going on for so long. I’ve even been through the painstaking task of setting both devices up from new, getting everything set up exactly how I always have it. Might work for a week or so, then it just stops again for new reason. Found out earlier that Messages alerts were turned off from my partner-I’ve *never* done that, because she’s the one that messages me the most: but it had been activated. Not by me!