I have a Note 20 Ultra and Galaxy Watch 3. I've restarted both numerous times, and this has been happening for weeks. When I get text messages often they go to my phone, but not my watch, I've always had them going only to my watch when I'm wearing it. If I open the messages app on my watch there won't be new messages, but if I set my phone down and walk away, when my watch disconnects from the phone and connects to LTE or wifi all of a sudden ALL of the texts I've gotten all day suddenly start coming up on my watch, so if I've gotten 20 texts that day, I will suddenly get 20 consecutive notifications and texts on my watch. If my watch is disconnected from my phone it will get the texts in real time, but won't receive them while connected.
I too have this problem with my Samsung S10 and the Galaxy watch 3. Very fustrating. The watch works fine when I turn off bluetooth, but then battery usage goes way up. I'd only get one day instead of three days when I'm connected to my phone.