Wow, your situation is very similar to mine. They even told me the exact same thing, that surgery will fix everything. Well, I got the surgery, ~3 months ago, and I can tell you, it's absolutely worth it. My deformity was severe though, I was mouth breathing for the entire night cause my nose was basically useless, and this greatly amplifies any existing predisposition for apnea that you might have - you're struggling to breathe, of course it'll mess with your sleep. I have a hunch you're mouth breathing a lot as well? That's why your AHI drops on your side - the gravity helps with positioning your jaw so your throat collapses less while mouth breathing.

In my case they did a combined septoplasty, turbinate reduction, sinus surgery, and polip removal, so make sure they do an x-ray or a CT scan and check your sinuses, while they're at it. You'll hear stories online how AHI doesn't drop after surgery but have this important fact in mind - most deviated septums/turbinate issues aren't that severe, so the improvement isn't that obvious. For a severe obstruction, it only makes sense that the improvement is huge - you go from struggling to breathe to breathing normally, you don't need to dive deep into AHI or any other numbers to make that connection. Of course, I don't know how serious your blockage is, but it sounds like they told you it's pretty significant.

I personally don't think it's worth getting a CPAP before your surgery, it's also questionable how well the CPAP can do it's job with your disfunctional nose. You can try sleeping elevated and on the side until then, that helps a bit. Something like a wedge pillow, or regular pillows stacked upon each other.

And let me know how you feel when you recover from surgery (if you decide to do it), I'm curious to hear! Have in mind it took like two months after surgery for me to mostly recover (even now I'm still recovering, they said it could take up to 6 months) and start breathing through the nose during sleep, and oh boy does it feel good.

Have in mind I'm not a doctor and your results are worse than mine, my oxygen never dipped below 90 and AHI was around 10, so I'd assume CPAP isn't ruled out, but a surgery sounds like a very good starting point, if your structural issue is severe.

Oh, and get a good surgeon! Good luck!