Thanks, Tom. When I do that, I’m not getting the apps. First, websites are returned, and Wikipedia, and other things. So I’ve been tapping the App Store option at the bottom of the list to go to there for the Open button. I also miss the old feature where the folder in which an app is stored is identified when you search.
I feel like there must be a setting I’ve overlooked, to have apps turn up in the Search, but I can’t find it. Here’s a screen capture of what I see when I search by swiping down.
And thanks for the tip about swiping through the dots! That’ll be quicker than going screen by screen if the swipe-down Search is functioning as intended.

NOTE: tapping in the item that shows “duolingo app” just opens another page of search results for the app 😕
Thanks.