Is ghusl obligatory upon seeing semen after waking up, with doubt as to whether it is a remnant of previous semen or from a new wet dream that was not accompanied by a feeling of deep sleep, and does a wet dream occur during light sleep?

There is no consideration for doubt during sleep, nor for doubt during slight sleep. Thus, whoever doubts during their sleep is not required to perform ablution (wudu’). Ritual purification (ghusl) is only obligatory with certain knowledge of sleep and the emission of semen. If semen was emitted after waking from residual seminal fluid from a previous wet dream, then it is more cautious to repeat the ghusl and make up the prayers that were performed before it. If it is known that she slept, even a little, and semen was emitted, then ghusl becomes obligatory, because the ritual impurity is attributed to the closest time it is likely to have occurred.