You used to be able to start dragging an icon from the home screen, use your other hand to open another app, then drop the dragged app over it to start split screen, but they nerfed it in iOS 13 for some reason. Completely undiscoverable of course, but at least it sped things up slightly. Having to open the second app full screen and then drag the other out of the dock's "recent" segment is just so clunky.
You can also drag an icon out of the search UI when you're in another app, but only if you have a keyboard attached, because other than Cmd+Space there's no longer a way to access Spotlight without going back to the home screen.
Even this way to open second app from the Spotlight start working only on the iPadOS 13.2.3. It was completely broken in previous releases as bad as dragging apps from the folders in the Dock.
You can also drag an icon out of the search UI when you're in another app, but only if you have a keyboard attached, because other than Cmd+Space there's no longer a way to access Spotlight without going back to the home screen.
Absolutely bonkers.