I saw an interesting Chizkuni the other day. In the beginning of parshat Pinchas, Hashem promises Pinchas a special covenant:
Chizkuni explains that this covenant of peace means that Pinchas would not have to fear from Zimri's relatives or Cosbi's relatives.
Alternatively, he would have to fear that he lost his priesthood because of the act of violence he committed, because a kohen who shed blood does not raise his hands. But Hashem promised him that since the killing was for the sake of Heaven, he could still function as a kohen.
This first idea, that he might have to fear from Zimri's relatives or Cosbi's relatives, relates well to the theme developed of their relative importance, as we read in a few pesukim (14 and 15), something echoed in the midrashic Putiel comments. This also calls to mind the reaction of Yaakov after Shimon and Levi's actions in Shechem.
Even so, I would guess that on a peshat level it is somehow synonymous with Brit Kehunat Olam.