When TNG Started, "our" Galaxy was tiny.
Now however, The Gamma Quadrant is explored or owned by a known quantity, the beta Quadrant is in the hands of the Klingons and Romulans, and the Delta Quadrant has ten percent being Borg Space, SOMEHOW 2 percent is Kazon, The Hirgen roam bout another 10 percent clinging to that communications network Voyager broke, but the Skirikans seem to have their grasp extending into the Beta and Gamma Quadrant.
The MIlky Way is Tiny.
Two dimensional thinking, GG?
My understanding is that the UFP, or most of it, is IN the Alpha Quadrant, but that does not mean they have fully explored, claimed and/or occupied all of it. Certainly, that is where most of TNG's adventures happen.
Ditto for the Klingons and Romulans in the Beta Quadrant. It might be "their" quadrant, for the most part, but that doesn't there isn't room for anybody / anything else.
As for elsewhere, seems to me that Voyager spent a fair whack of travel-time in space that seemed to belong to nobody in particular. The Hirgen have the remnants of a galaxy-spanning comm network, but holding territory and building infrastructure doesn't seem to have been a priority for a while. More like just a daisy-chain of commnodes / pitstops scattered all over, so they can do their macho hunting thing wherever they want. Given their way of doing things, I am unsure of their relevance in your assessment.
Two to four hundred billion stars in this particular galaxy (by current estimates). Not all of which have Class M worlds, of course, but even one percent cubed of that number would still mean a crapload (and current estimates are higher than this). Plus an unknown number of starfaring races, spacial anomalies, etc., etc., etc..
As Galaxies go, the Milky Way is a long way from being the biggest. But for we mere mortals, it is most definitely not tiny.
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