OK; I'll stick my head above the parapet of British class distinctions and usage
In my experience, it would be a matter of individual family preference as to whether room (A) would be called a drawing room or a sitting room. It meets the criteria for both, in that it has seating facilities [ie "sitting room"], and guests are entertained there [a prerequisite for a "drawing room"].
If there was another similar room downstairs [a family "snug"] where guests were not generally entertained, then that room would be the "sitting room", and room (A) would certainly be the "drawing room".
Neither room would ever, ever, be referred to as a "lounge".