On the s10 you can get to the search button when you swipe down one time on any screen. On the note 10 you scroll once the power and the settings appear on the upper right hand side but if you swipe one more time then it shows up next to the power button. Thats annoying, and its not like that on the s10
I am really confused... there is clearly a search icon in your second screenshot (the first screenshot is even more confusing). It looks like a magnifying glass, I just checked my phone and it's there, and it works as intended, so I must be missing something in your questions. Can you clarify?
Also smart things doesn't work like it used to on the S10, now you have to actually go into the app for wearables just to see the battery percentage on the buds or gear watch. Before it was right there when you slide down. SAMSUNG can you fix this?