Most hospitals send a summary bill (for example pharmacy: $5,000) hoping you’ll panic and just pay it. These are usually full of errors or huge markups. Before you pay anything, call the billing department and ask for an itemized bill with CPT codes. This will not only force a human to review it, but it also gives you the ability to spot BS. I tried this last year and the bill dropped by about 30% literally just because I asked, so don’t let them rip you off.
It’s still true in that the bill can go back and forth between the hospital and insurance and change.
I had a surgery about 5 years ago that started at about $45k, and every couple of days got the bill would change as things started getting picked up by insurance. Eventually it got down to just over $4k. I waited about a month and then still had to call insurance because my annual out of pocket was capped at $2k and they didn’t take that into account. Eventually it ended right around $1500.
This was all through the MyChart app, so it more it less does live updating after the initial bill is sent, opposed to a paper bill. Now I always wait about a month to pay any medical bills just to be sure, because if you over pay, you have to fight to get it back from insurance.