In-network hospital, out-of-network anesthesiologist - got hit with $9,800 surprise bill

Had a routine knee surgery in March. I did everything right - checked that the hospital was in-network, verified my surgeon was in-network, even called my insurer the week before to confirm coverage. Surgery went fine. Then about 6 weeks later I get a bill for $9,800 from an anesthesiology group I had never heard of and definitely never chose.

Turns out the anesthesiologist was out-of-network and billed me directly for the difference between what my insurer paid and what they charged. My insurer says this is my responsibility. The anesthesiology group says I signed paperwork when I checked in - which I did, but that paperwork didn't say anything about the anesthesiologist being out of network. Nobody told me that before the surgery.

I've read about the No Surprises Act but I'm confused about whether it applies here. The surgery was scheduled, not an emergency. Does that matter? Has anyone successfully fought one of these bills? I don't have $9,800 sitting around and the billing department keeps calling threatening to send this to collections.