PebbleOS has always had a feature called "Quiet Time" which does the same thing as "Do Not Disturb". Hopefully the new app will also respect the phone's native "Do Not Disturb" setting which has a bunch of nice automation features to e.g. turn on during meetings or at night automatically.
When you turn Notifications off for showing, they're just in the "inbox" & won't show on the watchface when received. You can then just access them whenever you want from the menu OR you can create a button shortcut that activates when pressing down.
FYI the previous generation of Pebble OS did not have a message counter, but this generation will apparently add this to its complications.
I wasn’t the one who wanted it, so you’ll have to ask them. I was just pointing out that you said “my watch accomplishes this” but it only accomplishes one of the two features they want, and honestly I’m pretty sure they know that you can silence notifications on most smart watches so the emphasis would have been on the second feature.