While I haven't seen it yet I can guarantee you there's nothing in 2002 Twilight Zone highlighting the fact that Whitaker was black, they just hired him because he was a good actor with enough gravitas to the Rod Serling thing.
Here's something really wild I just remembered, even Forest Whitaker wasn't the first black Twilight Zone host! In 1994 there was a made for TV special where they filmed two "lost episodes" of the Twilight Zone, scripts Rod Serling wrote but were never originally filmed and guess who was the host? James Earl Jones, so the Jordan Peele Twilight Zone was beaten by... 25 years.
That's one of the things that's dumb about modern Woke culture is people acting like they're breaking new ground when they're not.
I forgot to show my thoughts on the 1980s Twilight Zone, I've seen a few episodes, it's not great but they're were fairly interesting, the intro to that one is pretty cool although it's radically different from all the others, that coupled with no host makes it feel not much like Twilight Zone at all.
https://youtube.com/watch?v=2Znqt2b8CKQ
Monsters, what a great intro that show has, it's also always blown my mind how Tales From The Darkside's intro manages to make bright, sunny footage creepy.