States changing their borders

The real answer is that if both Oregon and Idaho agree then it may be done under the clause quoted in this thread or (I suspect) as a compact approved by Congress which effectively the same thing.

If Idaho disagrees to take on the counties it would be a moot point so the only interesting question is if Idaho agrees and Oregon disagrees with the transfer. Then it goes to SCOTUS under original jurisdiction but I suspect they would rule that as sovereign entities one state cannot annex another.

Although not the same exact scenario, the OP may want to look at the formation of West Virginia. Since it is up to Congress to guarantee a republican form of government, they chose to recognize a very unrepresentative body (Restored Legislature of Virginia created by the Second Wheeling Convention) as the government of Virginia during the Civil War and this body was the one that authorized the formation of a new state (WV).