

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”.

But given how recently they’ve dealt with Klingons, and especially given Nahla’s relationship with Obel Wochak, how much sense does being out of practice actually make? It’s not as if the Burn expunged all records of Klingon-Federation relations and the Federation had to rebuild from illuminated manuscripts copied by monks.
Don’t get me wrong - I liked the focus on the Klingons and it answered a lot about what happened to the Empire after the Burn. I’ve had a soft spot for the Klingons ever since John M. Ford’s The Final Reflection and the work that Ron Moore put in during TNG and DS9 and I was feeling really sad at seeing how far the Empire and the Klingon people had fallen.
I just think that the episode put too much heavy lifting responsibility on that last twist, because really, the solution was that obvious.
Now, I don’t profess to be a writer (not anymore), but maybe the structure could have been different. Of course the debate isn’t supposed to affect policy, but the cadets could have debated it differently, and the adults watching to see if they reached the correct solution which was obvious (to them) all along.
I remember when I was in the equivalent of my junior year of high school, and coming up with what I thought was a brilliant insight into Shakespeare’s Henry V, Part 1. All excited, I went to my English teacher and started blabbering about it. He listened patiently and let me finish, then said, “That’s great. You know, it’s been said before, but the important part is that you came up with it on your own.”
A possibility could be centering the core of the cadet debate not so much on whether or not they should force a solution on the Klingons (which as I said is a non-starter because the PD should have settled the question very quickly), but how to get Faan Alpha into the hands of the Klingons without violating their autonomy.
Then you could still get Caleb to take the side of “fuck it, what’s so good about the PD anyway?” and Jay-Den says, “But we have to remain who we are!”
And when Jay-Den has his epiphany, then the adults go, “Excellent. So this is what we’re going to do.” Because the adults have always known what had to be done but wanted the kids come to the conclusion on their own.
Then it doesn’t look like anyone is being an idiot.