I'm not really sure how much world events shaped the series of 2002. You could definitely say that shows like The Sopranos and The West Wing were influenced, but most of the ones I hung with were just coming into some strides that had long been established. It may be a better art form for reacting to the greater world than movies, but there will still be a delay and such a disparity of tones. Alan Sepinwall once wrote a piece about shows that defined presidential eras (Parks & Rec for Obama, for example). Trust that kind of historical documentation.
https://www.rollingstone.com/tv/tv-lists/president-tv-series-defined-era-994869/
Just missed the cut: Whose Line, Fairly OddParents, Steve leaves Blue's Clues