Daystrom Institute

There is the breakdown in Klingon relations, but that seems to be a common motif (like in "The Visitor"), and it's more of a cold war status than a Borg, Dominion, etc. kind of threat.

Otherwise, we don't have enough information on this timeline to firmly establish events. However, I infer this might be a timeline where the Dominion War was averted (or delayed) and Martok never became chancellor, as that event was sort of like another Narendra and if it didn't happen, a relationship deterioration with the Empire.

Evidence of this is in LD with Ma'ah's opinion that the Federation "earned its toduj" in the Dominion War, suggesting that event swayed his opinion on the Federation and likely others. This coculd be countered by the actions of Dorg and Bargh, showing that the views aren't universal. However, I think the relative level-headedness Bargh's fellow council members suggest that the brother's views are not a mainstream political view in the empire, at least in the 2380s.

(You could probably use STO stuff as counter to my argument, but I think the timeline of that game is motivated by a desire for a plot amenable to gameplay. I'm primarily going with alpha canon.)

As I said before, we can be certain that the "All Good Things" timeline was averted by Picard being aware of it, and that all timelines after are not that timeline.

Notably, Commander Nog appears with a TNG uniform and DS9 combadge... in 2389. This suggests that this timeline at least skipped First Contact, early 2380s, and mid-to-late 2380s uniforms, opting to keep the TNG uniform in for decades. This is kind of weird considering "Endgame", which I'll reconcile later. Anyhow, perhaps uniform designers had been toying with something like the prime early 2380s design; due to its longer time for development, when it was finally rolled out much later than prime, it manifested differently from its closest prime counterpart.

I think we can infer once again that the Dominion War was averted. For one, there's the reasons I provided above. I also think DS9 would sort of be sacred ground for the Klingons and it would feel almost wrong to them to take it outright if the Dominion War had happened like prime. The suggestion is further made by the fact that the Federation withdrew from DS9 in 2374, which would have been during the Dominion War in the prime timeline; this never would have happened with the wartime Alpha Quadrant alliance.

Additionally, we can tell the war never happened like prime because the Defiant was never destroyed - we can tell because they needed the ship to be basically the same to replicate the accident, and it was, judging by Jadzia's nostalgic reaction in the episode. If it were the second Defiant, there would have been differences as noted in DS9's "The Dogs of War".

Thus, basing on the first two timelines, it would seem like this uniform tends to arise when there are few mysterious threats, only regular ones.

To reconcile, it might be possible that in this timeline, the First Contact uniform roughly replaced what would have been the expanded life span of the TNG uniform (with error bars of a few years or so due to butterfly effect) instead of being slowly phased out in the early 2380s. Once again, the uniform concepts for what would have been the prime early 2380s uniforms were festering in the designers' heads as early as the mid-to-late 2370s and went through a similar development cycle to "The Visitor"'s timeline.

The state of Klingon relations in this episode is further evidence pointing to the role of the Dominion War in Federation-Klingon relations - B'Elanna's role and influence as a Klingon liason (based on Janeway's request) as well as Janeway's initially relatively easy dealings with Korath suggest relations are in a good state in this timeline with the Dominion War.

Despite the Dominion War happening, this timeline seems like it's also somewhat peaceful (only based on vibes, not canon analysis), considering that everyone on Voyager is either still in touch or dead - if this was one of those Picard-y timelines, at least would be a moody vigilante ex-Starfleet officer in some far off corner of the quadrant where no one can contact them.

The fact that this uniform never appears again after this timeline suggests the early return of Voyager was the final straw for this uniform. We can't pinpoint exactly what happened, but I can think of a few different scenarios. The most likely one is something about Voyager's early return triggered a shorter design cycle of the future uniforms, leading instead to the early 2380s uniforms. Alternatively, maybe some key designers of that uniform got butterflied into a shuttle accident, or the timeline got so depressing that they decided to pump out DS9-looking uniforms instead.