I think the main thing we have to keep in mind is that everyone must be far too confused to have any real agenda at this point.

I mean, these societies were going about their business as normal, then suddenly the Federation started making a fuss about the Borg, so everyone stuck their fingers in their ears, then the Federation started being annoyingly persistant and essentially bullied everyone into joining them and--HOLY CRAP, BORG INVASION, WE'RE ALL GOING TO DIE AND-oh, wait, it's all over. And now the Federation is suddenly- within about a day- lying half in ruins, as are the Klingons, and we're all standing around with our mouths open in shock and thinking "well, the Gorn might be odd looking and annoying, but I'd rather have them standing beside me if something like that ever happens again". And then realizing "isn't that what the Federation always said?" This must be really confusing.
They perceive the Federation (rightly or wrongly doesn't matter) as an overbearing holier-than-thou superpower restricting and confining them, economically, territory-wise, philosophically, whatever. The Borg crisis merely reinforced their idea of the Federation as a bully who just happens to smile and speak pleasantly- yet it also proved in rather shocking fashion that the Federation has the right idea (even Tezrene admits up-front that the Federation is the model for the Pact, at least in terms of basic concept).
The Tholians and the Breen, and the Gorn and Tzenkethi and Romulan Star Empire, have spent many decades - or centuries in some cases- feeling confined and restricted by the Federation and its expansion, as well as the Klingon's aggression (the Kinshaya seem to base their entire foreign policy on "fight off Klingons"). Whether they have cause to feel so threatened and frustrated is another thing. Some of the Romulans clearly desire the old days of conquest and feel frustrated that the Federation sprung up and halted them in their tracks- other Romulans seem content to keep the empire as it is now but fear the Federation anyway- after all, might not closer ties with the Federation lead simply to Romulus becoming a second Vulcan? The Gorn seem highly territorial, but not expansionist. They don't seem to have a quarrel with the Federation- indeed, the Black Crest which
did had to violently topple the ruling Crest before it could act- but they clearly find the Federation's "soft imperialism" a threat (see Ambassador Zogazin's comments in "Mere Mortals" about Qo'noS having been annexed by the UFP). The Breen are a mystery, of course, but we know the Tzenkethi have a near-insane fear of Federation expansion (or at least that's the
Tzelnira's favourite demon with which to scare the populace). I don't think the Kinshaya really remember the Federation exists most of the time (I think their worldview overall seems to be "There's us, the Klingon demons we fight, and, oh, also a load of other unimportant stuff out there in the wider galaxy")
The Pact members have had quite a shock, I imagine. They had a powerful opponent (or at least a rival), who is polite and friendly but overbearing and moralizing and who is scooping up territory and resources at an alarming rate. Plus, the big, tough bruiser (Klingons) is standing at their side and looking menacing. Suddenly, this powerful opponent is set upon by an
insanely powerful outside force which cares nothing for the petty politics of the region, and before their very eyes the rival has the crap beaten out of them. It's obvious everyone else is next, but then the threat's over suddenly. So, for the first time ever, the Federation and Klingons are lying there in a bloody heap and there is no longer any threat to anyone else (the Borg are now gone, after all). There must on
one level be the desire to scream "now's our chance! Kick them while their down!"- which the Kinshaya of course quickly embraced. But it's nowhere near that simple, because the Borg invasion also proved the Federation was correct in trying to get everyone to stand together. The rival is finally down and beaten, but it's finally been made clear that the rival was in fact
right, and that their way
works. So what do the Tholians, Breen, etc, do? Where do they go from here?
The confusion must be intense, and there must be so many feelings to come to terms with as a society: relief that the Borg didn't reach them, excitement at the new opportunities in a galaxy where the UFP and Klingons are no longer holding everyone else back, glee that the "overbearing" Federation got a bloody nose, shock that the Federation had it right all along, and above all the possibility of looking at their neighbours in a new way. The entire situation must be as confusing as hell!

I doubt the peoples of the Pact quite know what to do- everything's changed, and they're probably still trying to work it all out. They've thrown this historic union together so quickly, they probably can't even be fully sure what it is they're truly doing. They probably aren't even sure how to relate to one another yet, much less the tricky question of "what do we do about the Federation?".
I mean, the Breen and the Romulans hate each other- this is well established in the novels. But now Tal'aura won't accept aid from Donatra (a fellow Romulan) but she apparently
will accept it from the Breen and the (no doubt "lesser") Tholians and Gorn. What? And, wait, aren't we Romulans?, cry the traditionalists- is it not our destiny to one day rule over all the lesser peoples? Now you tell us the giant crystal scorpions and green lizards and colourful griffins are our
equals? In that case, who are we, then? The internal struggles and difficulties must come first, then the question of how this Pact is going to work- I'm guessing the Federation question is a distinct third to most (a few particularly spiteful Tholians excepted).