Since y’all are name dropping lol, my insurance is State Farm and theirs is Mercury.
Let State Farm handle it. They do this every day.
Would you pay a Dr or a lawyer for years just in case you got sick or needed legal advice, and then when you did not follow their direction?
Let your insurance company handle it for you. Your rates will not go up because of a subrogation claim. If someone told you they would they lied.