The PD applies to everyone the Federation encounters, pre- or post-warp.

The PD prevented the Federation from intervening in Bajoran internal affairs (DS9: "The Circle"). It prevented the Federation from intervening in the Klingon Civil War (TNG: "Redemption"). It prevented Picard from interfering with the Kaelon tradition of elder euthanasia, despite Lwaxana's entreaties (TNG: "Half a Life") and with the Ligonian's racist culture (TNG: "Code of Honor"). Kirk assured the Vians that even though they were more advanced than the Federation, the PD applied to them as well (TOS: "The Empath").

The pre-warp and post-warp distinction is not about whether or not you get to interfere; it's just the useful and most common criterion for first contact, i.e. when it is likely safe enough that first contact - revealing the existence of aliens - will not immediately alter the social and technological order. And a world that has achieved warp drive will be finding out about aliens soon enough. And even then it can be assessed that a civilisation still isn't ready (TNG: "First Contact").

At the end of the day, the PD is about non-interference, period. TOS even calls it the "non-interference directive" in TOS: "The Apple", "A Piece of the Action" and "Patterns of Force". Picard calls it that in TNG: "Justice".