I think this proverb roughly means that a wise man isn’t lonely even if he is without company. However, when considering its construction, my understanding is starting to get shaky.
Let me explain what happens in my mind.
My daughter is no less talkative than my wife is.
My wife is (very) talkative. That’s true. However, my daughter might be more talkative.
The speaker wants to emphasize his daughter’s talkativeness.
A wise man is never less alone than when alone.
A wise man is lonely when he is without company. That’s true. However, a wise man might be lonelier.
Of course, I can’t understand my explanation at all. I’d be happy if you could tell me about its construction.