OBGYN Nurse practitioner is considered specialty but doctor in the same office is not?

So I have an established OBGYN who I have seen several times. Up until a few months ago, I have always seen the doctor, and it has always been a $40 copay for office visits, which is the standard copay for a non-specialty office visit on my plan.

A few months ago, I had a semi-urgent matter come up and needed to be seen ASAP. So the office booked me in with the first practitioner who was available, who was a nurse practitioner. At the time of the appointment, they charged me my standard $40 copay, which I paid.

A few weeks after my appointment with the NP, I was billed an additional $20, so $60 total ($40 which I paid at the time of the visit + $20 that they billed later on.) When I asked the dr office about this, they said it was toward a copay. When I pressed further, stating that my copay for standard office visits is $40, they said it’s because they are considered a specialist.

My plan does indeed have a higher copay for specialists and it is $60. However, upon reviewing my plan’s details, the coverage for the $40 includes things like physicals, pediatrics, and OBGYNs/women’s health.

I spoke with an agent from my insurance (BCBS) and after researching it for over an hour, he finally agreed that it should be a $40 copay and sent the claim for review. That was over a month ago.

I followed up about it today, and the person I spoke to initially couldn’t even find the claim under review. She said she would call me back, which she did, and she informed me after researching it further, she discovered that the specific provider who I saw last time (the nurse practitioner) is considered a specialist, while my actual doctor is not.

This makes NO SENSE TO ME. Can someone please explain this? Or advise how I get this fixed, if it’s an error?