So it comes down to an independent Skyrim kicking the [censored] out of Thalmor out of Skyrim, which is a VERY attractive outcome.
Though having a less than fully weakened Empire to one day [censored] the Thalmor in WW2 is also VERY attractive.
Or it could come down to
The Thalmor conquer an independant Skyrim and go on to dominate the already weakened and increasingly destabilized Empire.
Or the Empire stays together but in the end it is for naught and the empire ceases to exist as it is know under the Thalmor.
Or Skyrim gains independance for a time but the Empire eventually retakes it (perhaps Ulfric creates own division). Then the Thalmore gets involved.
Next game takes place in Thalmor dominated province/home province or in Hammerfell.
Or Skyrim becomes independent and the Thalmor avoid it and take down the Empire.
Or Skyrim stays with the Empire but can't save the Empire so becomes independent after it falls.
Though Hammerfell is likely to aid the Empire in a war against the Thalmor, would Skyrim do so as well? The Empire didn't outright make war with Hammerfell, and Stormcloak is the rightful high king of Skyrim in accordance with the old nord ways.
Apprently a lot of Nords disagree he is the rightful High King in accordance with the old Nord ways - it wouldn't be much of a civil war if Ulfric was obviously in the right.
Oh and the Empire tried to cut off his head. So if Skyrim became independent, how would Bethesda write that into the lore, unless the next great war happens in a few generations after Skyrim takes place?
How detailed does the Lore need to be?
Also which one is more likely to be written as what officially happened? Its not like one is more obvious than the other. Unless the next tes game just doesn't mention much about the civil war other than a vague footnote?
Hard to say - of course some people would complain - "I did this, why doesn't future game recognise what I decided to do (my cannon character sets all lore!). But not me.
The last three ES games haven't really been about the PC redefining the politics of the age or vastly changing the political/cultural structure as such (Skyrim has come closest to that). You have a big picture objective (stopping Dagoth Ur, stopping the invasion through the Oblivion Gates, stopping the world being eaten by dragons) - in the course of doing that you move through the culture and politics, perhaps have an immediate impact in that immediate time/place and immediate future but you don't take over Morrowind, don't get put on the throne or any of that.
You stop Dagoth Ur in Morrowind, the rest is personal detail. You help close the Oblivion Gates, the rest is personal detail. You save the world from Dragons, the rest is personal detail. In Morrowind regardless of which house you put on top through your actions or who you kill the fate of Morrowind is the same.
Maybe the easiest thing would be to have it set far enough in the future where the outcome's ripples have died down. Just have a conversation early in the game that will set a limited number of lore related objects. While a prisoner someone asks you something and mentions the Skyrim civil war. You have an option of saying something about Imperials or something about Nords. Depending on which you select the lore books switch over and relate to one side winning or the other. Whoever won doesn't have much impact on the game at hand though (though again I imagine cannon obsessives not liking that).