You can definitely shop around and ask the different providers (doctors and surgery centers) how much they would charge if you pay cash.
I had to have an MRI done, with my insurance (HSA plan also), they wanted to charge $900+, I asked what happened if they didn't file the claim and that I paid cash, they said it would be $350. So with insurance $900+ which is the network negotiated rate, with no insurance $350. I said I'd take the $350. I paid for it from my Health Savings Account but it did not go into my deductible even though they were in network, but because it was cash pay, I got a much bigger break. Providers purposely jack up the prices because insurance would pay, but they charge less for cash pay patients. Not only this, years ago, same story, on another service. Always ask about the cash pay price if you want to pay less. I even called my insurance company to complain about this, they said those were the prices they signed in contract with the providers, they couldn't charge less.
You have to have an HSA already opened, you don't have to fully fund it first, but it has to be opened first, and then have the surgery, and then fund it and reimburse yourself.
Whatever you have leftover in your HSA when you turn 65, if you want to take it out for NON-Medical use, you have to pay tax on it like a traditional IRA. A PP is wrong on this. If you use it to pay for IRS approved medical expenses, then no tax, or if you use it to pay for Medicare Part A and Part B, no tax.