I had similar problems with a specialist. Their appointments are typically six months out, and if you need something more urgent, the answer is "sorry that's all we can do." My last actual appointment, after the ~six-month wait, was a simple 15-minute telehealth visit. It's insane.
I have great insurance and I've never had any problem paying. It's amazing to me that doctors seem to really push back against having patients, or their patients having appointments. Isn't this how they make money? What kind of weird market effect incentivizes this behavior?
It's interesting that dentists and oral surgeons seem to be the opposite. I've never had a problem finding one and they usually seem welcoming, happy to help, and glad to have the business.