Is it obligatory to cover the 'awrah during the prostration of forgetfulness (sujood as-sahw)? May Allah reward you.

The prostration of forgetfulness (Sujud al-Sahw) is part of the prayer, and its validity requires the same conditions for the validity of prayer, such as ritual purity and covering the 'awrah. Prostration is not valid except with purity from minor and major ritual impurity and physical filth (najis), covering the 'awrah, facing the Qibla, and having the intention, based on the Prophet's (peace and blessings be upon him) saying: "Allah does not accept any prayer without purification." And because it is a prayer, these conditions are stipulated for it.