clarify others for anyone who examines and reflects upon them.

In short, two matters must be distinguished here:

The first is an individual worshipper’s supplication, such as that offered by someone performing the prayer for guidance or other prayers, and the supplication a worshipper offers individually, whether leading the prayer or following an imam. The second is the imam and congregation supplicating together. There is no doubt that the Prophet, may Allah bless him and grant him peace, did not do this second kind after the obligatory prayers, as he did the remembrances transmitted from him. Had he done so, his Companions, then the Successors, then the scholars would have transmitted it from him, just as they transmitted matters of lesser significance.

Hence, later scholars held differing views concerning this supplication:

Some regarded it as recommended after the dawn and afternoon prayers, as mentioned by a number of followers of Abū Hanīfah, Mālik, Ahmad, and others. They had no Prophetic precedent to cite for this; their only argument was that neither of these two prayers is followed by another prayer.

Others regarded it as recommended after all the prayers, saying that it should not be recited aloud unless the intention is to teach. This was mentioned by a number of followers of al-Shāfiʿī and others. They have no Prophetic precedent for this, beyond the general consideration that supplication is prescribed and is more likely to be answered after the prayers. Yet the Lawgiver has already taken this consideration into account within the prayer itself: supplication at its end, before concluding it, is prescribed and established as a sunnah