Don't be distraught.
I had the same concerns as you before my surgery. I have a large sliding hiatal hernia/gerd. Some days I have a hard time bending over to tie my shoes.
I'm also a long time smoker. I had no problem at all
during or after my surgery.
I can't remember if I was given my regular prilosec when I got there, or if they told me to take it with a tiny sip of water before I came, but no problems with reflux either.
I'm also large-breasted and have a big stomach, so I was scared to death that I would have a lot of trouble - I was afraid I'd smother. Not at all. Although I did have oxygen for a little bit in recovery because I think the anesthesia and pain meds depress your breathing sometimes. It was short-lived though, and from what I understand pretty common no matter your size.
If your hospital is like mine, you'll also get to talk to your anesthesiologist before surgery. (ask at your pre-op what the procedure is - I did.) Mine came around and reviewed all my meds with me and why I was taking all of them. Then would be a good time to tell him about your concerns. I know they intubate us and all - just don't know all the specifics. I do know that we're all hooked up to all kinds of monitors, so I know if you were having any breathing difficulties due to pressure they'd know.
They're very conscious about gerd too - due to aspiration concerns and have a cocktail of drugs that help to prevent that. Plus, not eating the night before helps tremendously.
BTW, I had a LAVH BSO TVT - and I'm pretty sure I was upended for quite a bit of time to get all that done.
I am very glad I had the LAVH and not abdominal - that's such a much longer and difficult recovery.
I hope this helps. Good luck with your surgery, see you on the other side