In an old WordPress posting I found the property dialog image at the bottom of this post (labeled "Properties"). It was displayed for a vertical bar chart (single series).
It includes property Visible under Labels.
But in the present day (in an up-to-date version of ReportBuilder with no "About" information), in a Stacked Area chart, the Series Properties dialog appears as shown immediately below. There are many fewer properties, no "Labels" section and no "Visible" property for labels.
I can choose "Show Data Labels" and there are label properties, but again no "Visible" property.
Is a Visible property exposed "somewhere else" for a Stacked Area chart?
I'm not sure whether I should think of this more as a limitation by SSRS chart type, or more a stripping out of features in later versions of SSRS Report Builder.
I started down the path of putting an expression on more than one of the label properties to try and achieve an effect similar to "Visible", but I decided to post here before going to those lengths.
Input from somebody with SSRS insights much appreciated.
The first image you posted is the properties dialog box. This typically shows common properties with a nice UI.
The second image you posted is the properties panel which shows all properties of the selected object.
Taken from Report Builder MS Documentation :
To see the Properties pane, on the View tab, in the Show/Hide group, click Properties.
You might also find that the 'Visible' property is actually called Hidden
for some objects, just to confuse things further !