Out of network surgery with OON benefits, how much should I expect back?

Hi, I navigating surgery bills and I am looking for advice

I had an out of network surgery with a specialized doctor.

I have out of network benefit (plan pays 70%, I pay 30% plus balance bill), I knew that I’d be paying for some of the procedure.

Insurance pre-certified this procedure

Prior to the procedure, I paid a deposit of $18,400 – the minimum the doctor was will to accept

The actual procedure was $13,360.00

EOB shows Provider Discount which brings the insurance payment to $1590.50 after the discounts. The EOB says patient responsibility is $0

2 questions:

How much should I be getting back? The full $18,400 because my insurance paid them and it does not say I owe anything OR $6,630.50 ( $18,400 – (13,360.00 – 1590.50))

The doctor’s office is asking me to sign an OON payment agreement LR document that I didn’t sign prior to the surgery, do I actually need to sign this now that they’ve been paid and the surgery has already happened?

The document states the following: In the event that your insurance carrier payment is not sufficient to cover the minimum payment indicated In the eventunar vour insurance carrier payement is not sufficient to cover the minimum payment indicated above, you would be responsible for the difference between the minimum amount and insurance reimbursement. This minimum amount required is to protect you so that you are not burdened to pay the total charge amount; however, in the event that your insurance carrier pays more than the minimum amount we will not balance bill you