Are the aforementioned clothes considered pure, or is it necessary to rewash them and ensure the purity of the water draining from them, given that the black trousers are heavily dyed and were washed with other black clothes, one of which had impurity, and they were washed twice in the automatic washing machine?

If impure clothes are placed with pure clothes in a washing machine, all of them become pure if the impurity is completely removed. As for the water changing color due to the garment (dye), it does not affect the purity, as long as the change is due to the dye and not the impurity, as Al-Hattab Al-Maliki narrated concerning the wash water of an impure garment.