FWIW I had surgery for this a couple years ago and have not had issues. My insurance (US / Providence) did cover it. There was some criteria that had to be met based off an ultrasound. It was explained to me as a measure of how much time per pulse blood flowed the wrong way.
The surgery was pretty much unnoticeable (the method was the cauterization technique someone mentioned). I also had the veins stripped from one leg after - they were very extensive on that leg. They were likely going to disappear anyhow but it was towards the end of the year and the out of pocket max was hit and I just wanted it to be done with. Also not painful, but a very… interesting… feeling.