The new bottom screen behavior:
A quick short swipe up from the bottom returns you to the Home Screen.
A short swipe up with a pause brings up the dock.
A short swipe up and continue to the left or right will scroll between recently opened apps.
From the Home Screen you can bring up the last app by swiping up and to the right.
A longer swipe and pause goest to the multitask screen.
A little practice makes it easy.
Getting to the Home Screen is the quickest getsture. The general consensis is that either Apple is moving towards more consistant gestures accross all iOS, or they are preparing for the demise of the Home button on future iPads.
The iPhone X acts somewhat like this.