I tend to assume it refers specifically to the "hot war" started by the Na'kuhl in "Storm Front," which led to the resolution of the Temporal Cold War.
Yeah, true. I forgot in Enterprise it was generally referred to as the "Temporal Cold War". So far, at least from what I can recall, I didn't see anything in
Wonderlands that conflicts with your DTI stories (or at least anything major). It'll be interesting to see if your DTI works can co-exist with the show. On one of the Enterprise boards there is speculation about "future guy" and some think he's a future Archer (I don't particularly care for that one because there were times Archer could have been killed by Silik or the Suliban which doesn't seem to make a lot of sense if it were a future Archer--and it just seems out of character to me). I prefer your revelation over Archer. Not sure if Discovery tackles things that specifically or not but something else I'll find out I suppose.
I think it's mainly just to explain why the Burn couldn't be undone with time travel, and also to underline why the Discovery crew can't go back to their own time. The last two episodes of season 2 made it explicit that the ship's trip to the future had to be permanent, but there were still lots of viewers who missed or disbelieved that part and assumed it would just be one more reset-button time travel plot like all the others. So season 3 took time travel decisively off the table right up front to underline that the move to the 32nd century was not going to be undone.
The show did seem pretty clear closing out season 2 that this was a permanent move, though I see your point. And when it comes to the current showrunners, you never know what they'll do next. But I didn't think they were going back. I wonder if part of the reason for that is to free them a bit from the continuity box they were in setting it so close to the original series. Being in the 32nd century pretty much allows them to do what they want since there is very little continuity to worry about with that.
Now of course we do have at least 2 more shows coming out in the 23rd century (assuming the Section 31 show is still a go, along with Strange New Worlds). But perhaps the current show runners want to make sure it's more in line with what we recall from that period. Discovery presented some things that were created that didn't seem to fit all that well (like my persistent bugaboo....spore drive....

). Since they are creating Strange New Worlds and the Section 31 show, they have more freedom to keep things more consistent with the original series if they wish.
But in any event, Wonderlands itself seems to make clear that she isn't going back. I definitely got the sense, even without seeing season 3, that they are there to stay.