The only good news is that this is flagrantly an act of war. You don't move armada sized forces in an attempt to annex a superpower's neighbours (And that's flagrantly what they're doing) and not expect the other side to react to it
Which means that we're liable to be able to draw on the member fleets more heavily for this.
Like, the HoH pulled this because they smelled weakness, that we didn't hold our ground when it was untenable out of ideals--and thus, those ideals are obviously weak and easily absorbed. I think this was actually a blunder on their part brought on by a lack of ability to get in the Federation's head--because they would go to the knife on their ideals at the drop of a hat, even if it's not geopolitically sound to do so.
You don't need much to hold your own ground when nobody who isn't assured loyal is allowed to have starships that can survive on their own longer than a few days.
And when you've got enough internal control on top of that to the extent of "Everything you say is believed implicitly", all you need to do is wipe out anyone who protests and claim it was the act of someone else, and all is well.
More importantly, they're just confident they have enough social control at this point that they can say "We've always been at war with EastAsia" with a straight face and expect everyone in their populace who matters to agree.
That and the neighborhood survivalist is going to start pulling out all the stops because their not going to like this one bit