Correct, when you swipe downward on your Home Screen and search for an app that way, you cannot relocate it.
Try this method:
From your Home Screen, swipe left until you get to the App Library.
Swipe downward and you'll get an alphabetical list of your apps.
Locate the app in the list or type the app name into the search field
Once you've located the app, tap/hold until it raises/selects, then drag it and it'll pop out to your Home Screen
Organize the Home Screen and App Library on your iPhone - Apple Support
Something else that may help you.. When you download new apps, if you want them to show up on your Home Screen rather than getting tucked away in the App Library, go to Settings > Home Screen and check Add to Home Screen rather than App Library Only