Why should this be a problem? DSC was written half a century after TOS. The failure of DSC to, say, "conclude Spock's story" did not much impact the writing of TOS. OTOH, the writing of TOS was source material for DSC, despite the newer show's events taking place earlier in the fictional universe. Fiction is flexible that way.
...Why?
How the war ended had zero impact on ST:INS. The movie was not obligated to tell any specifics, and never did. The two things we can infer from the movie, and the writers could assume, would have been that the UFP and Worf would not have died yet. Only the latter involved any sort of real betting, and
a) I doubt Dorn would have gotten himself kicked out of the show by shouting "I was in the movie, Worf is immortal, you can't refuse my raise!" or by meekly agreeing to die at the writers' whim (I mean, Worf is immortal, explicitly appearing in most of the futures shown in Star Trek), and
b) the writers betting wrong would not depend on whether the war was over or not anyway: if Worf could die, he could die in any DS9 episode, in the middle of the war, after the war, in a time travel adventure before the war...
And conversely, when the Borg invaded Earth in ST:FC, on DS9 nobody noticed much. This is neither a contradiction nor a problem.
Timo Saloniemi