I was trying to read a value that is modified to include different custom properties into one (in this case the Property Name is 'Material'):
I fail to get the value to be shown in the property tab builder though, because it shows the text expression only:
Is this one of those missing things or am I doing something wrong with the property tab builder?
You are doing nothing wrong. You are missing that property tab builder displays the value/text expression field not the evaluated value field. So, from my experience using this functionality, what you are trying to do, cannot be done.