I think that's just a result of the term falling out of common use in the US. I'd expect 30 years ago "Spooks" would be a perfectly fine name for a TV show in the US. (I remember watching spy shows/movies and reading spy novels as a kid in the 80s/90s and hearing/reading that term.)

It generally doesn't. People should stop reviving the negative connotation. Sure if someone is calling a black person a spook let's call them out but if that's not how it's being used let's not insist it's an inherently racist term. It's totally counter-productive.

Not what you are doing, and I understand that's why they renamed the show but they shouldn't have. While it can be used as a racial slur it doesn't generally have that connotation. I think if you directly asked most people they would either not know about the slur or say something like "I think its a racist term for some group or something." I had to look it up myself to be sure. We can choose to let that usage of the term die.