Subrogation and Government Claims

My vehicle was damaged by the county. They have fought me tooth and nail, first denying liability then making a lowball offer ($3k on 10k damage). I’m ready to give up and file the claim through my comprehensive coverage, but I am concerned about a rate increase.

The facts and evidence are 1000% in my favor, but they (county) have engaged in coverup activity and other misrepresentations that have obfuscated the record. I’m concerned that Progressive won’t aggressive,y subrogate and it will end up on my record as an at fault. I can handle the deductible, I am more concerned about rate increases.

So my questions,

If Progressive decides to just pay out the claim and not subrogate, will my rates increase like an at fault determination?

Would telling the County I am going to file the insurance claim encourage them to pay the claim, or have the opposite effect? (As in, are they more afraid of fighting Progessive than me)