Why won't my new MBP actually shutdown when I click "Shutdown..." in the "apple" menu
I'd start with resetting both the NVRAM and SMC (in that order). Before following the steps below, ensure you have no external hardware connected and that you're using the built-in keyboard.

Reset the NVRAM

Reset the NVRAM on your MBP as follows:


Fully shut down your MBP. 
Press the power button and then press the commandoptionPR keys. You have to make sure you press these keys before the gray screen appears or it won’t work.
Hold those keys down for about 20 seconds or until you see the Apple logo
Let go of the keys and let your MBP reboot normally.


Note: When you log back in you may need to readjust some of your system preferences (e.g. speaker volume, screen resolution, startup disk selection, time zone information, etc).

Reset the SMC


Fully shut down your MBP. 
Press and hold the power button for at least 10 seconds
Let go of the power button and wait 5 seconds
Power up your MBP again


Once you've reset the NVRAM and SMC use your MBP as usual and see how it behaves when you shut down etc. If it's still misbehaving, reset the SMC again but with the following steps instead:


Fully shut down your MBP. 
Press and hold the right shift key and the left option and control keys for 7 seconds before then also pressing and holding the power button down for another 7 seconds (i.e. the keys will end up being held down for 14 seconds, the power button for 7 seconds)
Let go of all three keys and the power button
Wait 5 seconds
Power up your MBP again


If all of the above doesn't work, it may be worth testing your MBP in Safe Mode to see if it behaves differently to how it does normally.

Boot into Safe Mode 

Follow these steps to boot your Mac into Safe Mode: 


Fully shut down your MBP. 
Restart your MBP
Immediately press the Shift key and keep it down 
Let go of the Shift key when you see the login window (NOTE: If you have FileVault enabled you may need to log in twice). 
Take a note of what happens (i.e. does your display wake up normally, etc) 
Exit Safe Mode by restarting your MBP as normal 
Test again when booted normally 


If the problem doesn't occur while booted into Safe Mode, let me know and we'll go from there.