The baku did not settle unclaimed space.
Because when this space was claimed by the klingons, they would have searched their new property and evicted these few hundreds of luddites with extreme prejudice, especially considering what a clement/valuable M class world these luddites were on.
Except from the data Soong found in the Klingon database the Klingons were aware of two inhabitable planets in the Briar Patch and they didn't move to take them, probably becuase it would be more trouble than it is worth as they would have to move ships into a difficult to navigate area where you have to travel a considerable distance just to communicate with the rest of the galaxy (so basically its Bumf@#k Idaho in space), and they only thing they would seemingly get from all the effort it would take to move in is some particles which go against their philosophy of dying gloriously in battle.
So no I really don't think the Klingons would bother with a backwater planet of little importance (to them probably) thats hard as hell to get to.
One does not have to inhabit the planets to claim them - much as you don't have to be on your land to claim it as property.
As to the notion that the klingons - or the romulans - won't claim VERY valuable real-estate such as M class worlds in their space as their own -
Before the klingons, the briar patch belonged to the romulans. T'Girl went into detail about it - short version, same considerations as with the klingons apply.
The baku remain tresspasers; they are very far from being able to invoke adverse possesion. BTW, you don't need to cloak a planet for your possession to be hidden; merely hide (not announcing your presence and, generally, trying to stay under the radar) on a small patch of the planet (as the baku were doing by their own admission).
And, as said, tresspassers are evicted - no compensation required. BTW - tresspassers are also the ones entering your land - not only your house.
Squatting is about occuping an abandoned piece of real-estate; and the briar patch is - and was - claimed as property by various polities.
Must a court of law decide over eviction or eminent domanin? Of course.
And considering the situation (billions vs. 600), guess what would the quite moral decision of any court of law be? The baku are relocated + given access to the immortality drug and the rings are harvested.
But wait: The baku don't agree to hyposprays for immortality - it's against their luddite philosophy! They want it to come 'naturally', on the land they tresspass on. And they don't care that billions will suffer and die for this.
As repeatedly said in this thread, the only reason the writers didn't went this route is because they didn't want to telegraph the entitlement complex of the baku. That doesn't stop you and other posters from using this smokescreen of an argument repeatedly, though - along with moving the goalposts vis-a-vis ~'federation law may be different', etc.