Ok so Foresee is clearly for initiative where as farsight has force power die to add to vigilance checks. But doesn't call out initiative, so my question is does farsight add force rating to initiative rolls if it's a vigilance roll?

Yes.

Foresee adds Force Dice to both Cool and Vigilance but only during Initiative rolls (or any other skill that for some reason is being used for initiative)

Farsight adds Force Dice to ANY Vigilance check, including Initiative.