What is the ruling regarding the prayer of the congregants who continued their prayer with the Imam after the Imam intended to leave it upon remembering that he was not in a state of ritual purity, whereupon he performed tayammum and re-entered the prayer with a new opening takbir, along with mentioning the evidences?

If the Imam remembers during the prayer that he is in a state of ritual impurity (hadath), he should withdraw, perform ablution (wudu'), and return to pray. It is valid for the congregants to continue based on the initial following, as the Messenger of Allah, may Allah's peace and blessings be upon him, did when he returned to prayer with water dripping from his head, and the Companions did not repeat the opening takbir. If the Imam prays while forgetful or ignorant of his state of ritual impurity, his prayer is invalid, but their prayers are valid. If the Imam suffers from an illness or injury that prevents him from washing a part of his ablution limbs, and there is no splint or plaster, he must wash the healthy limbs and perform tayammum (dry ablution) for the injured area. If he does not do so, his prayer is invalid, but their prayers are valid. Prayer with tayammum on painted walls is not valid due to the absence of dust.