Is it permissible to recite the Dhikr immediately upon the limbs settling in prayer, and does the prayer become void if one does so, given the presence of whisperings (waswas) that prevent immediate recitation after settling?

The fundamental principle is that the remembrances (adhkar) said in prayer should be recited immediately after commencing the action, such as bowing (rukuk), prostrating (sujud), standing (qiyam), and sitting (julūs). This is because it is what was authentically reported from the Prophet, peace and blessings be upon him. Whoever delays them has acted contrary to the Sunnah, but delaying them does not invalidate the prayer.