Manu Smriti itself,which existed since Krita, mentions those rules.
So,it can not be that Sutaka rules emerged only after the Mahabharatha war which happened in Dwapara.
The following are few relevant verses from Manu Smriti.
Manu Smriti 5.83. A Brahmana shall be pure after ten days, a Kshatriya after twelve, a Vaisya after fifteen, and a Sudra is purified after a month.
Manu 5.75. He who may hear that (a relative) residing in a distant country has died, before ten (days after his death have elapsed), shall be
impure for the remainder of the period of ten (days and) nights only.
5.79. If within the ten days (of impurity) another birth or death happens, a Brahmana shall remain impure only until the (first) period
of ten days has expired.
Foods given by certain persons are not to be accepted.Few among them are:
Manu Smriti 4.217. Nor (the food given) by those who knowingly bear with paramours (of their wives), and by those who in all matters are ruled by women,
nor food (given by men) whose ten days of impurity on account of a
death have not passed, nor that which is unpalatable