Billing issues between the hospital and Blue Shield California

I had a surgery on June 20th. I paid my estimated responsibilities of $3,400 on the morning of the surgery day. The hospital had informed me of the patient estimated responsibilities which was the remaining amount of my out-of-pocket maximum, so I happily paid it because it would allow me to go see doctors without paying for the rest of the year. I have Blue Shield California HMO with $0 deductible.

A few weeks after the surgery, my insurance company mailed me a finalized bill stating that my responsibilities were $2,500. As the hospital owed me $900, I filed a claim with the hospital on July 14th.

What happened is that the hospital and the insurance used different ways of calculating, which created the difference. Per the hospital, the insurance needs to pay more to them. They also have a claim with Blue Shield, and they requested to reprocess and have been following up regularly.

They say there's nothing I can do for the claim between them and I need to wait until it gets finalized.

What frustrates me is that I’ve already paid the out-of-pocket maximum this year, but according to Blue Shield’s system, I haven’t. So I can neither get my medical expenses covered nor receive a refund from the hospital.

This is my first time being in this situation. If you can share your experience and knowledge in this area, I'd appreciate it!!