@Milan-Šádek the same as Garmin says, but it is only half of the truth. You can do the simple (or lazy) approach, to send every notification to the watch as you get them from the notification center. But you could also implement a filter between the notification and the push to the watch. Or even inside the watch.
I get that iOS possibly limits you to find out what apps are installed, so you cannot choose in the beginning. But I remember the Galaxy Watch Active2, where I could define on the watch that I never want to have a notification from “this app” again, as I got a notification there. So it would be possible to build a blacklist even directly in the watch, if the notification is pushed to the watch directly from iOS…
As @SimonDe says other companies go that extra mile…