How to quickly switch between two apps on one half of the split-screen view?
Tested on Oreo 8.0. lt works as described without destroying split view

Try EAS App Switcher
it creates a floating icon that can be hidden as well and find it particularly good in switching to previous to previous app , that is juggling with three apps ; 

In Settings Single tap on second icon &rarr; switch to second last app does this

It prompts to you to change the home which makes it faster. It doesn't support gesture navigations that you are looking for but offers some like fast pull to display notifications etc