Is ghusl required upon waking if white discharge is found, whether thick or scant?

Ghusl is only obligatory upon certainty of seminal discharge. The characteristics of a woman's semen are detailed in Fatwa 102977. If you doubt whether the discharge is semen, madhy (pre-seminal fluid), or vaginal moisture, you may choose and assign it the ruling you prefer, as explained in Fatwa 118035. It appears that what you are experiencing is ordinary, pure vaginal discharge, which necessitates wudu' (ablution). Please refer to Fatwa 90938.