In fact it sounds like the Klingons weren't that interested in the area at all either.
Well the Klingon Empire was interested enough in the area to fight the Romulan Empire for it, and win it in battle. Prior to 2270 the area was
the Romulan's, when they acquired it (and from whom) is unknown.
It's impossible to say if the area was unclaimed when the Baku party arrived, it might have been, or the Romulan could
have held it at the time, or another interstellar power perchance.
Would the Baku have expended any effort in ascertaining the exact disposition of the "property" they settled upon? It seems unlikely they would have tried to, it might have advertized their presence.