One of the style categories in Writer is _section_ styles. When examining content inside a section with a certain style (whether unnamed/DF or named style) - the style inspector shows _no_ aspects of the section style (e.g. background color or indentation).
I was of two minds whether the of visibility of all style categories is an effective desideratum that is not being met or not. Decided to err on the side of leniency, so marking this as an enhancement request.