Is the story of Al-Ala Al-Hadrami and what he did with his army – as mentioned in "Al-Bidaya wa Al-Nihaya" – authentic, and can it be considered evidence for the permissibility of congregational supplication after prayer?

This report mentioned by Ibn Kathir, without a chain of narration (isnad), cannot be used to derive a ruling. Even if it were authentic, it does not indicate the permissibility of collective supplication (Du'a) after prayer, because it occurred due to a specific calamity, not because of the prayer itself. The commonly practiced collective Du'a after prayers is an innovation (bid'ah) because it has not been authentically reported from the Prophet (peace be upon him), and because those who do it believe it to be recommended at this specific time. As for an incidental collective Du'a, there is no harm in it. Shaykh al-Islam Ibn Taymiyyah differentiated between recurring gatherings that resemble prescribed acts of worship and are considered innovation, and incidental gatherings that are not taken as a habit. This report is not suitable as evidence for the permissibility of collective Du'a after the five daily prayers, due to its weakness and because the Du'a in it was for an incidental reason, not due to the prayer.