Android 13: Swapping apps in split screen and adding new apps

*Not a duplicate of https://android.stackexchange.com/questions/253087/swapping-windows-in-split-screen-mode since it is Android 12 specific (I actually wrote out an answer for this without realizing the question is for Android 12 and instead of wasting the efforts in answering, I decided to make it a self-answered question).* **As in title, how do I switch apps from top pane to bottom pane (and vice-versa) as also add a new app?**