Acute Exacerbation of Heart Failure: Given the patient's history of systolic and diastolic heart failure, severe aortic stenosis status post TAVR, and pulmonary hypertension, an exacerbation of heart failure is a plausible cause for his symptoms of shortness of breath and chest tightness. The patient's complex cardiac history predisposes him to decompensated heart failure.

Atrial Fibrillation with Rapid Ventricular Response (AFib with RVR): The patient has a history of atrial fibrillation and is on anticoagulation with Eliquis. AFib with RVR can lead to symptoms of shortness of breath and chest discomfort due to inadequate cardiac output and increased heart rate.
Stable Angina or Acute Coronary Syndrome: Although the patient has a history of CAD status post PCI, the presence of chest tightness could indicate either stable angina or an acute coronary syndrome, especially if there has been a change in his angina pattern or if the tightness is new or worsening.
Pulmonary Embolism (PE): While less likely given the lack of specific risk factors mentioned (e.g., recent immobilization, surgery, or known thrombophilia), PE can cause shortness of breath and chest pain and should be considered, especially in a patient with atrial fibrillation who is on anticoagulation.

Aortic Dissection: Although rare, aortic dissection is a life-threatening condition that can present with chest pain and shortness of breath. The patient's history of severe aortic stenosis and TAVR, as well as hypertension, increases his risk for aortic pathology.
Cardiac Tamponade: Given the patient's history of TAVR and severe cardiac disease, cardiac tamponade is a potential, albeit rare, complication that could cause shortness of breath and chest discomfort due to impaired cardiac filling.
Pulmonary Hypertension Crisis: A sudden worsening of pulmonary hypertension could lead to right heart failure, presenting with shortness of breath and potentially chest tightness.

Mitral Regurgitation due to Papillary Muscle Dysfunction: While less common, significant mitral regurgitation could lead to heart failure symptoms. This could be a consideration if there's a new murmur or if echocardiography shows significant mitral valve dysfunction.
Constrictive Pericarditis: This is a rare condition that could present with symptoms of heart failure, including shortness of breath and chest discomfort, especially if there's a history of pericardial disease or recent cardiac surgery.