Hospital billed $14,000 for a 4-hour ER visit - insurance only covered $1,800 of it

I went to the ER in January because I had severe chest pain. Spent about four hours there, they did an EKG, some bloodwork, a chest X-ray, and gave me IV fluids. Turned out to be a panic attack - which honestly made me feel stupid on top of everything else. They discharged me and said I was fine.

Last week I got the bill. The hospital is billing $14,240. My insurance paid $1,800 and applied $600 to my deductible, leaving me with an outstanding balance of $11,840. The EOB says the hospital is "out-of-network." I had no idea. There's exactly one hospital within a reasonable distance of my house and it's this one. I didn't exactly shop around while I thought I was having a heart attack.

I've since learned there's a law called the No Surprises Act that's supposed to protect people from exactly this situation for emergency care. But when I called my insurance company they said the hospital has a carve-out or something and that's why I owe so much. I'm so confused. Did they apply the law correctly? Is $11,840 actually what I legally owe? I can't pay this and i don't know what to do.