this doesn't really matter, but, normal english would be either "Why are people all (of) the sudden writing browsers with AI?" or (slightly less normal) "Why all (of) the sudden are people writing browsers with AI?", with the (of) being more 'correct' but often omitted. Regardless, it should be "are people" instead of "people are" in a question.

(In edited writing, “all of a sudden” is far more common than “all of the sudden”. https://www.merriam-webster.com/grammar/usage-of-all-of-a-su...)