it seems like samsung havent gotten smartthings ready for galaxy watch 3. i can find the app on my galaxy watch, but not on my galaxy watch 3, hope they get i fixed soon.
I recently got a Galaxy Watch 3 too, and I can't find the SmartThings app on the Galaxy Store (I can't even go into my owned apps and look for it). I can control my SmartThings devices with Bixby on my watch, but for some reason the app isn't there.