Regarding "pulmonary arterial hypertension" there are various levels/groups of pulmonary hypertension - depending on cause (see link below). It is important to have correct diagnosis to determine if there are medications and who should treat it. For example, I have pulmonary hypertension group 3 - caused by my pulmonary fibrosis so I have a Pulmonary Specialist in Interstitial lung diseases for that not a Cardiologist.

Right Heart Catheterization is the gold standard for determining if one has pulmonary hypertension and degree. If your transthoracic echocardiogram (TTE) mentioned pulmonary arterial hypertension then it is understandable why they are talking to you about a right heart cath. It is a serious disease. I am surprised your primary provider would voice an opinion as not qualified. You do not want it to get worse! I would look for a pulmonologist experienced in treating pulmonary hypertension (they all do not!).

Unfortunately, one has to find the Specialist with the right subspecialty. My first local pulmonologist signed off on a report that was confusing and said I had both restrictive lung disease and COPD which is an obstructive lung disease. But five more pulmonary function tests at different provider all say I don't have COPD!
https://www.mayoclinic.org/diseases-conditions/pulmonary-hypertension/symptoms-causes/syc-20350697