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I do think you have the right approach, won't we have issue with all the other segue overriden? I don't remember exactly how it was working.

Because Segue doesn't support @IBInspectable , we have to set a default value for one Segue, the walkaround is to create different segue for different Presentation.

If the current Segues only support fullscreen, shall we change the method func present(animated flag: Bool = true) to func presentFullScreen(animated flag: Bool = true)?

I can rename but I will make my mode less intrusive, so it is not always fullscreen

Set fullscreen only if in automatic, so if someone choose explicitly an other presentation it will continue to work. And if he want to have issues he can choose pageSheet :)
But to compile with xcode 10.3 I must do something, maybe use rawValue of automatic of check on swift version 5.1...

I has made my code more restrictive to fix the segue but!

I see that fixing the segue is not the solution
In you test the demo app, which is not using segue, the Transition part failed to "present" things too. The same code is used after all

Maybe some code to fix into UIPresentationController override or delegates

In Xcode 11.3, I had to apply the Presentation fullscreen setting onto specific View Controllers in order for the segue to complete successfully. Making sure to use the custom segues from IBAnimatable now works again.