IMO an iguana like yours, at her age, who had good care all it's life is not frail soley due to being 9 years of age. The vets are used to seeing igs who are in very bad shape due to lack of proper care, and 9 years is beyond the expected lifespan. But it's true that any ig can't have anything but an emergency operation when it is severely anemic.
Hand feeding can be a trap, as you may know. They get used to the new way of feeding and can't instantly go back to chowing down a plateful of veggies. I understand your need to do something tangible to care for her though. So for now, keep it up, and give her lots of water. Always give her a plate of her favorite foods and treats.
Campbell's Soup makes a veggie soup. Feed her the fluid portion of it to keep up her electrolytes. My vets heartily approved of that. I don't think she needs more than 3 cc's each day, but it could be lifesaving.
Spaying only cures the problems of malfunctioning reproductive systems. It's not always a cure for anemia. But for an otherwise healthy ig, a needed spay at nine years is OK. Before she can have her spay, she needs to have the anemia reversed as much as possible.
There is one case to be made for spaying/exploratory surgery. This is if she is consistently losing ground, and the surgery is the only hope. Death in the operatory may be preferable to living a long, painful end-of-life illness.
I had a long-term female who started acting sick which only got worse. She got antibiotic injections along with 6-week courses of antibiotic pills. She had this treatment about four times, until the vets had a meeting with me to point out that she likely had an invisible infection the antibiotics couldn't cure and probably had an abscess that was killing her. So there was no choice other than surgery while she was sick and weak. What they found were infected eroding ovaries and the infection had spread throughout her gut cavity (very painful peritonitis). They got her cleaned up, did the spay, and she survived. But she just as easily could have died on the table. It took her six months to start eating on her own again. This is the positive side of surgery as a last-ditch cure.
I know nothing about swollen jowls. IMO disregard it.
Supplements "may' help, but the most common results are hypervitaminosis, body inclusions, and bladder stones. Igs are created to eat large amounts of low-nutrient foliage/fruits. She can go much longer than you think with low eating.
One thing you can do to increase her immune function is to raise her temperatures a bit, like by 5 degrees. Make sure she still has a cool zone.
I assume her antibiotics make her better for a short while. If so, all in all, if this were my ig, I would find a way to go ahead with the spay, which will give the vets a good look at her innards. Find a vet who has done at least thirty iguana (reptile spays in general) spays. Don't put her in the hands of a vet who has done only a few.
This is the best I can do. I surely do hope she survives this thing.