The Typhon Pact, looking at it as powers forming together for mutual benefit, are very much like the European Union. Not in antagonism to the US (which is very much like the Federation, member states/worlds, standard set of laws, etc) but in addition to it. If you look at Star Trek's admittedly sketchy history prior to United Earth, there are supposed to be only a handful of small unions, The European Hegemony, the African Union or whatever it was called, the United Arab Emirates, and so on and so forth, but these unions did not form the UE. Each individual country signed up and, with Australia supposedly being the last hold out until 2150.
Who knows, by the end of the 25th century, the individual members of the Typhon Pact, the Klingon Empire, might have all signed up for a new alliance, with each member world of the Federation doing the same for a true Pax Galactica.
But it will take time.