The legitimate Klingon government asked for help and the Federation said no.
From The Last Outpost...
DATA: They should add that Starfleet has permitted several civilisations to fall. We have at times allowed the strong and violent to overcome the weak.
There was no ongoing genocide or threat of such during the KCW. It was an internal conflict over political succession. You're acting like it's the same thing. It isn't.
Robert Maxwell wrote:
If the Ba'ku never got a distress call out to anyone, of course, it's a moot point.
They'd never have to. Any Federation influence aside, Starfleet isn't going to allow a collaborator of its enemy to loiter in an part of space it perceives as its own, no matter how remote or hostile an area it is.
Assuming the Feds noticed, given the remoteness of the Briar Patch (and the fact that what goes on in it is not readable by outside sensors.)
Methinks the Federation would be happy to smack around a known Dominion collaborator for picking on the inhabitants of a backwater planet in Federation territory, though!