I was skeptical of the new home button and app overview - (why fix something that already works pretty well?) - but it actually looks good and seems to actually improve the experience.
When I see UI changes like this my initial concern is not for myself but for my 75 year old mother. It has taken her years to be able to move through Android with some efficiency and the basic consistency has been a good thing. A fundamental UI change like this isn't as easy for users like that to adapt to. I am already dreading the first time she has a Google P based phone. I hope to be proved wrong.
The new swipe-up-from-Home UI is off by default. I had to turn it on in Gestures. By default, it's the old three-button UI: Back, Home, App switcher.
Tapping Home and tapping Back still do exactly the same thing. Long-pressing Home still opens Google Assistant.
Opening the app switcher UI is now done by dragging Home up (instead of tapping App Switcher).
Quickly switching to the last used app is now done by dragging the Home button right (instead of double-tapping App Switcher).