Is it permissible to remember Allah while one's 'awrah is exposed or in a state of nudity, such as during the remembrances of waking up or exiting the lavatory, or upon hearing the adhan while one's 'awrah is uncovered, by analogy with uttering the Shahada during the ritual bath after major impurity (ghusl from janaba)?

A Muslim should cover their 'awrah (private parts) when performing dhikr (remembrance of Allah), characterized by dignity and tranquility. However, the uncovering of some 'awrah does not prevent the recited dhikr, as covering the 'awrah is not a condition for the permissibility of dhikr. Rather, dhikr is مطلوب (recommended/sought) upon waking up, exiting the lavatory, removing clothes when entering the lavatory or bathing, and repeating the adhan. As for reciting the Shahada during ghusl (ritual bath), it is not among the prescribed dhikr and should be avoided inside impure places.