Is it not incumbent upon one who has performed ghusl with water that has been used for istinja' (purifying oneself after defecation or urination) to wash their body again with other clean water for prayer, considering water that has been used for istinja' to be impure?

The default state of a Muslim's limbs is purity. The water used to wash their limbs does not become impure unless the impurity of the limbs is established and the water changes due to that impurity. Thus, washing water that has changed due to impurity is impure, whereas water that has changed due to dirt or dye is pure. The majority of scholars hold that water used for removing ritual impurity (hadath (definition)) is pure, though they differ on whether it is purifying (tahūr) or not. Therefore, it is not obligatory to wash the body with clean water merely because the water has been used by another person. Water used for removing ritual impurity is not impure, but according to some scholars, it is not permissible to use it for removing ritual impurity again.