Couple of things here.
First of all, it has to do with the nature of "space war" in general. Both the Federation and the Klingons only ever fight wars over disputed planets that both of them seem to want. The Klingons generally haven't set their sights on that many planets that are claimed by the Federation other than Arkanis and a handful of others; if they were going to war at all, it would be over those.
So how does that war stretch out to more than twenty years, all because of the Battle of Narendra-III? That suggests the "war" as we understand it is more complex than we really believe and a lot's going on in the background that isn't being mentioned.
In which case:
Nob Akimoto wrote:
It seems likely to me, that the decline of the Federation in this timeline probably stems from having to fight a multi-front war while facing a power with rough parity like the Klingons. It seems unlikely that simply going to war with the Klingons would put the Federation so badly on the back foot, especially since (although some 2 generations earlier) the military brass in the 2290s were confident the Federation could "clean the chronometers" of the Klingon Empire and the weakness of the Klingons in general around the Praxis incident.
Meaning it probably isn't just the Klingons. Just a couple of years after the Narendra-III massacre, the Federation and the Klingons are at war.
Picard knows about the Romulan attack in the prime timeline, but not in the new one. It's likely that the Romulans were in the process of forging an alliance with the Federation at the time, aggravating the relatively peaceful relations with the Klingons. A squad of Romulan warships slaughtering a Federation starship would have torpedoed (literally) any such alliance and resulted in the Klingons cozying up to the Federation in an "enemy of my enemy" sort of relationship. But if nobody knows the Romulans killed the Enterprise, that alliance might have finally come to pass.
20 years ago, that would have cleared the way for a Romulan invasion of the Klingon Empire (of which the Khitomer Massacre would have been merely an opening move). Hard to say where that goes after twenty years, but it seems evident that the Klingons not only survived the Romulan invasion, they recovered enough that they are now seeking revenge against anyone and everyone who ever supported the Romulans in any way shape or form. It's likely that most of that war involved the Federation and the Romulans teaming up against an increasingly powerful Klingon military; the current "downfall" stage of the war is a consequence of the Klingons finally overcoming the Romulan empire, glassing Romulus and then turning to the Federation saying "And now it's YOUR turn!"
Also, I'm pretty sure that Deanna Troi was part of the Enterprise crew when it was first commissioned. She was killed by Armus on Vagra-II in an attempt to get an emotional rise out of the Enterprise rescue team (Deanna, being the only person on the entire crew with a high regard for sentient life).