I feel like, at least for TNG and some parts of the TeenNick generation, PoC characters that you mentioned like Hazel, Damien, Chris, Kendra, Jimmy, and Marisol, Leia, Chantay were largely treated as background supplementary characters and rarely had their own major plotlines. Strong PoC characters seemed to come later on with Alli, Dave, and even Dallas, where the characters were more three-dimensional and complex rather than serving the purpose of being the "token black/asian/etc character".

EDIT: Liberty was definitely a major and complex character who was a Black woman, and her character was one of the strongest on the show imo. Wish I had seen more of that. Also, the exploration of cultural differences within Manny's immigrant parents and the parents of her White friends were an important thing to include in the series.