Got a $4,000 surprise bill from ER visit - thought I went to an in-network hospital

Went to the ER at my in-network hospital after a bad fall. Turns out the ER doctor who treated me was OUT of network even though the hospital is in network.

Now I'm getting a bill for $4,000 for his services. My insurance says I'm responsible because he wasn't in network.

I didn't choose this doctor! I went to the hospital I was supposed to go to! How is this legal?

I've heard of the No Surprises Act - does that help me here? How do I even start fighting this?