There is a lot of information here and this post will be long so message me with questions. This comes from years of working in all three categories of Insurance, Collision Center, and Law Enforcement so I've gone through this a few times.
First, if you are not at fault, and there was a police report stating, you need to go through the insurance company that started this mess. For example, if Car A hits Car B and Car B is the one that hits you, Car A is at fault. Now, police officers have terrible training, and most of the time they want to go the easy route so they will list it as Car A is at fault. Now, if both Car A and Car B were shooting a stupid TikTok and being typical hood rats and both hit you, the LEO can place blame on both parties, resulting in the crappy 50/50 agreement. Or, this is the most common, the LEO doesn't know what happen but knows you're the claimant or victim, he can place blame on both parties.
Scenario #1:
This is what should happen. Don't tell State Farm shit. You will talk to some mouth breather who is terrible at their job and are the first rung of the ladder. They are told to make a claim and transfer to a field or DRP/Open Shop assignment to, a local to you, collision center. Then you will do all the wonderful leg work (that won't stop by the way) and then pay your deductible when it's completed and you pick the car up from the shop.
Scenario #2:
You use the police report and make two phone calls. Both of the calls will be to the other parties' insurance. They will then provide an estimate, which you will provide to the other company so they can take care of the remainder. This is by far the worst choice but releases you from dealing with SF and paying your deductible. Subrogation is a long process and especially now that there are two companies taking care of the claim. Also,
subrogation is nice and all but does take time. Now, insurance companies, once they are paid, will reimburse your deductible but I've seen that process take weeks up to a year.
The easiest path would be to get the two insurance companies to agree with each other, which it sounds like they are both agreeing that their policyholders are at fault. Then choose one company to get the vehicle repaired through and then those two companies will split the bill AFTER you are back in your vehicle. None of that crap matters to you so they can do it on their own time.
Good luck.