How to shut down MacBook Pro when logged out

The OP seemed to be asking how to shut down from the “login screen”, before amending the question. I was simply answering the question in the way it was asked. From the login screen is a perfectly acceptable way to perform a shutdown, because either no apps were open (from power on) or the user is warned about programs closing automatically and loss of unsaved data before logging out.

Are we even talking about the same thing? I meant the little icon on the login screen that shuts down with a click.

Did you read the info at the link? It says to use the on/off button if the other methods don't work.

"Turn off (shut down) your Mac

The best way to shut down your Mac is to choose Shut Down from the Apple menu .

Just as your Mac follows a startup process after it turns on, it follows a shutdown process before it turns off. That process includes automatically quitting all open apps and logging out of your macOS user

account. 

If your Mac doesn't shut down, try Force Quit to close any apps that aren't responding. If that doesn't work, press and hold the power button until the Mac turns off.

Press and hold the power button to turn off your Mac only if it isn't responding. You'll lose unsaved changes to any documents that you have open."

You won't lose any changes because you are already logged out.

There should be three symbols at the bottom of the login screen. I see it whenever I power up or when I log out.

I'm running Mojave 10.14.5 on a 13" non-Retina mid-2012 MBP. I see these at the bottom of the login screen. Do you see this?

Those instructions don't show the "Shut Down" button, but I can verify that one should be able to shut down by clicking on the symbol, unless there's some problem and there no mouse or trackpad function.

I get it now. The way would be to unlock and then shut down. I believe the assumption made with the lock screen is that the user should be able to unlock it before shutting down - possibly saving all unsaved data. When I log out, I get a message that says that all unsaved data will be discarded.

Why would it need to show the "Shut Down" button? The "Shut Down" button is located in different places on different model/year computers. The point is that when other options to shut down are not available then use the "Shut Down" button.

How to turn your Mac on or off - Apple Support