Question about prior auths and switching insurance

30FTM, NYS, Cigna for the remainder of this year.

I have a feeling that I know the answer to this question, but I want to double check. I’m in the process of consulting with a surgeon for a hysterectomy. It’s not an emergency procedure, so I don’t know how quickly I’ll be scheduled. My employer is switching insurance from Cigna to BCBS in 2023. I’ve gotten the letters my current insurance requires from my providers advocating for the procedure and the prior auth has been started with Cigna. From what I was told, it can take around 4-6 weeks (maximum) to get approval from insurance and get scheduled for this surgery.

If my insurance switches in the new year before I’m able to get the actual procedure, it would be safest to push out the surgery date further until I can resubmit to my new insurance with their own prior authorization, correct?

Is it possible to keep the surgery date and submit proof afterwards that I was approved by my former insurance, or would that not matter to the new insurance (and risk me being on the hook for the surgery not being covered)? As it’s a gender affirming surgery, I believe NYS is required to cover it either way, but I don’t know if a prior auth mistake would risk voiding that rule.

TIA.