The part that still remains on the phone is part of the LCD module. Due to it being a poor quality part they have become seperated so the LCD frame is left on the phone and you have just lifted the LCD itself. You will be able to lift that frame off just as if you were removing the whole thing. Just get a thin tool underneath the plastic bezel and start lifting from the bottom and work your way up. The clips you highlighted are how the screen is held on so this is completely normal and should come away with some light prying. And also please make sure the 2 pentalobe screws at the bottom of the phone (either side of the charging port) are removed.
Have seen this a few times and on every occasion it has been the Charging Flex Assembly. This is not too hard to do with the correct tools or any mobile repair shop should be able to complete this repair. Samsung Galaxy S8 I/O Daughterboard Replacement
According to your own diagnostics, unfortuantely it does look like the Home Button Flex is at fault here. It is actually a fairly common problem after replacing the screen. In my experience I have always found it to be the IC on the Home Button Flex (U10 - Turtle IC) and have replaced a few of these myself although is a difficult repair. Also, I am sure you are aware, but you cant just replace the home button on these models as both the Home Button and TouchID functions will be gone. You can buy 3rd party buttons such as the JC products, but these will only bring back Home Button functionality, but not TouchID.