It's not really a war against the Klingons, it's more of a Klingon civil war, and since the federation is allies with the Klingons they have an obligation to assist the Klingon government.
The rebel Klingons are actually from the past, "Discovery" era (which, as we all know, doesn't fit with any Star Trek canon). I won't hold that against her though because she makes a hela cute Klingon.
Star Trek Online has been one of the few places where fans can see real Star Trek. Even though these poorly though out shows (like the JJ movies or Discovery) have come along, the people working on Star Trek Online have done a much better job of it than CBS or Paramount have done.
I still think that, if they were smart, they would invite the people who made Axanar on Youtube to make a movie or series. The fans would love it, and judging by what they have done so far, it would be much better than anything from CBS or Paramount over the last 10-years.