It is possible to have both inflammatory arthritis and PMR. I have multiple autoimmune disorders. Having one autoimmune disorder doesn't exclude a person from having another one. In fact, it is more likely that you will develop another one over time.

My original diagnosis was more than 30 years ago. At the time, my diagnosis was called Reiter's syndrome but the name has been changed to Reactive Arthritis.
https://www.aafp.org/pubs/afp/issues/1999/0801/p499.html#:~:text=Reactive%20arthritis%2C%20also%20called%20Reiter's,of%20patients%20with%20reactive%20arthritis.
"Dr. Reiter" did human experiments during World War II and the syndrome no longer bears his name. The syndrome is now call "reactive arthritis" because it is triggered by an infection.

I see no reason why a covid infection can't trigger polyarthritis. I was diagnosed with PMR about 20 years after being diagnosed with reactive arthritis. My rheumatologist said it was unfortunate to have both PMR and inflammatory arthritis.

From personal experience, I would say it is extremely difficult to distinguish one from the other. My rheumatologist asked me if I had muscle pain or joint pain. When I couldn't say definitively, she seemed to understand that it was difficult for me to know. She based her diagnosis of PMR on other things. PMR wasn't based on a fast response to prednisone because reactive arthritis responded the same way. However, my rheumatologist wanted me off prednisone in the early stages of PMR so she could see exactly what symptoms I was having.