I'm having no such issues with the Galaxy watch 4 classic 46mm Bluetooth version and the s21 fe 5g,
I have gone through the notification settings in the wearables app and trimmed down the apps I want notifications from, gmail/TEXTS/calls/SS health etc are all getting pushed to my watch.
I hope you get to the bottom of it,
I'd check power saving measures (battery optimisations) on your phone and load the app store on your watch just to make sure your apps are upto date, even though I have my watch set to auto update I still find apps waiting in there from time to time