Earlier quoted context omitted.
You can add "Volume Up" and "Volume Down" keys, along with other useful functions, in the initial touchbar view by going to the settings.
I've been wanting to do this for ages, but I can only find the volume slider! Could you tell me how to put Volume Up and Down buttons on there please?
At "Touch Bar shows".... change that from "App Controls with Control Strip" to "Expanded Control Strip". Then you will see the individual buttons. You can then further "Customize Control Strip..." and you will now see more buttons. But you will also loose "App Control".
Of course, why can't those specific buttons be a customization option there with "App Control with Control Strip" forcing you to choose between volume up/down and "App Control"? Because Apple.