This is a proposed (and probably not fully thought out) interaction model to arrive at a split screen with two apps in iPadOS.
The model starts with a first app being opened in full screen.
Swipe up from the bottom of the screen gently to bring up the dock.
When a full screen app is showing and is capable of being split screened, the dock includes a new multitasking control icon.
Activation of this icon shifts the current fullscreen app to the left, exposing both the apps on the home screen and the dock, which stays present. Swiping of the home screen portion on the right side exposes different apps in other home screens.
When the app which is to share the screen with the now-split-screened app on the left is located, it can be activated.
Activation of the second app causes the app to open in the part of the screen unoccupied by the first app.