Is it permissible to recite the post-obligatory prayer remembrances (adhkar) in any situation, or is it only permissible while sitting after the prayer?

It is permissible for a person to recite the prescribed dhikr (remembrance of Allah) after the obligatory prayer standing, lying down, or in any state. Sitting is not a condition for it. If one recites it after standing up or while leaving, they have followed the Sunnah, and there is no harm in that. If one is distracted from it and then remembers it and recites it soon thereafter due to an excuse, it is likely that they will receive its specific reward. However, if one intentionally abandons it and then recites it after a long time, it is likely that its specific reward is missed, but the reward for general dhikr remains.