Well, as @sunking101 suggested use Edge Panel. I understand you want things to function exactly like the iPad with SlideOver. But sometimes it doesn't work like that and as I recall SlideOver detracts viewing from the main app.
Edge Panel is probably your best bet for situation like these... you can put whatever conversational app in the Edge Panel. Invoke the edge panel to use the conversational app whenever and add it as a SplitScreen window. Heck, you can even make app pairs from the Edge Panel.
Yeah I tried that and it is way too time consuming and cumbersome every time I do something to add a split screen and then remove it if I want to have the other app in full screen.
It doesn’t need to be exactly like SlideOver but I want to have the same functionality so that I can get to a chat app as quickly and in as few steps and then be able to hide it until I want it again. Right now I have to swipe and press once to start typing and swipe once to hide it so it’s around that level I’d want to be. Much more than that and I might as well consider the feature not being there and switch apps into full screen.