Actually there should be hundreds or thousands of other political groups equally as important as the ones we know of in the Alpha Quadrant, which is an entire quarter of the disc of the Milky Way Galaxy.
How many planets should there be in the Milky Way Galaxy which are naturally habitable for Humans? As far as I know, the only attempt to calculate their numbers was by Stephen H. Dole, in Habitable PLanets for Man, 1964, 2007. When scientists try to calculate the numbers of habitable worlds in the galaxy, they usually or always mean worlds habitable for carbon-based, liquid-water-using lifeforms, many of which, even on Earth, can and do survive in conditions swiftly fatal for unprotected humans.
https://www.rand.org/content/dam/rand/pubs/commercial_books/2007/RAND_CB179-1.pdf[1]
On page 104 Dole states that the probability of a star having a habitable planet is about 0.47 percent (O.0047), and that there are about 645 million habitable planets in the Milky Way Galaxy. Thus Dole estiamtes that there are about 137,234,040,000 stars in our galaxy.
At the present time it is estimated that there are 100 billion to 400 billion stars in the Milky Way Galaxy, and thus about 470,000,000 to 1,880,000,000 habitable (for humans) planets if Dole's calculations are correct. (And there should be several times as many planets which are habitable for some forms of carbon-based, liquid-water-using lifeforms but not for humans.)
And thus the Alpha quadrant should have about 117,500,000 to 470,000,000 habitable planets accoording to Dole's estimates.
Of course habitable planets are much more common in Star Trek than Dole estimated. Habitable palnets are so common, possibly having been terraformed by advanced civilizations in the past, that it seems likely that every star in Star Trek has at least one habitable planet.
So the Alpha Quadrant could have 25,000,000,000 to 100,000,000,000 planets habitable for humans and for intelligent beings with similar requirements.
Suppose that a space realm has 1 industrialized planet capable of building 1 space battleship per year.
it could 1 add space battleship to its space fleet every year, and keep every space battleship until it was destroyed or obsolete.
Suppose that a space realm has 1 industrialized planet capable of building 10 space battleship per year.
it could add 10 space battleships to its space fleet every year, and keep every space battleship until it was destroyed or obsolete.
Suppose that a space realm has 10 industrialized planets each capable of building 1 space battleship per year.
it could add 10 space battleships to its space fleet every year, and keep every space battleship until it was destroyed or obsolete.
Suppose that a space realm has 10 industrialized planets each capable of building 10 space battleships per year.
it could add 100 space battleships to its space fleet every year, and keep every space battleship until it was destroyed or obsolete.
Suppose that a space realm has 100 industrialized planets each capable of building 10 space battleships per year.
it could add 1,000 space battleships to its space fleet every year, and keep every space battleship until it was destroyed or obsolete.
Suppose that a space realm has 1,000 industrialized planets each capable of building 1 space battleship per year.
it could add 100 space battleships to its space fleet every year, and keep every space battleship until it was destroyed or obsolete.
Suppose that an interstellar realm has 1,000 industrialized planets each capable of building 10 space battleships per year.
Then it could add 10,000 space battles to its space navy each year, and keep them unil they are destroyed in battle or become obsolete.
And so on and so on.
An intersellar power with 1,000,000 industrialized planets each capable of building 1 to 10 space battleships per year could add 1,000,000 to 10,000,000 space battleships to its fleet every year. And yet still be only a tiny dot on a map of the Milky Way Galaxy.
In E.E. Smith's Lensman series the governments which ruled two separate galaxies fought each other with space fleets of millions of space battleships.
In the Star trek: Deep Space Nine episode "Sacrifice of Angels", in a major strategic battle, the Federation and allies had 600 ships and the Dominion and allies had 1,200 ships engaged. If those were about 10 percent of their side's total forces, the Federation and allies would have about 6,000 total ships and the Dominion would have about 12,000 ships in the Alpha Quadrant.
And I think there was a Dominion fleet of reinforcments of 2,000 ships coming through the wormhole. If that fleet was 1 to 10 percent of the total Dominion space navy, the Dominion would have had a total of 20,000 to 200,000 space warships.
The small space fleets combined with the allegedly large galactic regions that the various powers supposedly rule shows the truth of the TV Tropes tropes:
Writers Cannot Do Math
https://tvtropes.org/pmwiki/pmwiki.php/Main/WritersCannotDoMath[2]
and Sci-Fi Writers Have No Sense of Scale
https://tvtropes.org/pmwiki/pmwiki.php/Main/SciFiWritersHaveNoSenseOfScale[3].
Since I can do the math and do have a sense of scale, I say that there must be tens, hundreds, and thousands, of times as many powerful and important interstellar realms in the Alpha Quadrant as the ones seen in various Star Trek productions.