Does the worshipper's correction of the Imam after bowing, and the Imam's return to correct the recitation and then bow again, necessitate sujood al-sahw (prostration of forgetfulness) for the Imam and the congregants, and is what they did correct?

What the imam mentioned did by returning to correct his mistake in the surah is not correct, because its place was missed as soon as he bowed. If he returned out of ignorance or interpretation, his prayer and the prayer of those behind him are valid. But if he returned intentionally, knowing the ruling, then his prayer is invalid. As for the congregants, the preponderant opinion is that they do not need to repeat it, unless one of them knew that the imam intentionally violated the Sharia ruling. In the case of a valid prayer, the prostration of forgetfulness (sujud al-sahw) is legislated for the addition that occurred. If he returned to bowing after rising from it, he would have added an unlegislated bowing. If he did so intentionally, his prayer would be invalidated. But if he did so out of ignorance or forgetfulness, the prayer would not be invalidated and he should perform the prostration of forgetfulness. Reading the surah is a Sunnah in the first two rak'ahs, and the prayer is not invalidated by intentionally omitting it.