At the beginning of season 3, Rick teleports the Council of Ricks into the middle of the headquarters of the Galactic Federation. Was the organization he destroyed in this way the Galactic Federation of a singular dimension, (the one they fled to after leaving C-137 to the Cronenbergs) or a multi-dimensional entity?
No, although they are the primary controller of the Interdimensional Customs
The Federation has appeared a few times. First in the Pilot, when Rick and Morty travel through the Interdimensional customs which is primarily controlled by the Galactic Federation. (click to embiggen)
Although called the Interdimensional Customs, it seems to be more of a high speed way of travelling by using other dimensions to travel through. Nothing yet has suggested that the Galactic Federation from the Cronenberg dimension is the same as the Galactic Federation from the "new" dimensions. Or that they're aware of their co-existence. This is supported by the fact that in Season 3 Episode 1, The Rickshank Rickdemption, we find out that blue portals are only for regular travel and green portals are for interdimensional travel.
From the end of the below clip of the pilot, we see the Rick hacked the blue portal and turned it green.
More evidence is given in The Rickshank Rickdemption when the blue and green portals are clarified as seen below:
(ignore the ending I think it's some promotional nonsense)
While we have not seen any evidence my guess is they are not. The reason is in The Rickshank Rickdemption one of the major plot points is the Federation going through great risk to get their hands on Rick's portal gun. While it may be just better than their technology, most likely they need it because they do not have interdimensional travel.
Otherwise why go to this Rick? Just find one in some other reality that is more agreeable.
I am also assuming there there are many Federations, one in each dimension, they just can't work with each other