The nucleocapsid Ab is different from the spike protein Ab, so those will distinguish infection from vaccination. The T cell test is not widely available.... so getting the test isn't likely to convince clinicians one way or another.

palpitations alone, in absence of other symptoms, is probably just palpitations. you'd rule out a more abnormal arrhythmia with a holter, and then carry on with live.

Long COVID as certainly a constellation of symptoms in a syndrome, and it falls into various constellations - neurologic, dysautonomia, chronic fatigue, etc. There is no "test" to diagnose it... similar to fibromyalgia, and several rheumatic diseases...

... such is the nature of medicine. Physicians take a medical history and run confirmatory tests sometimes. 90% of the diagnoses is made in the mind of the physician based on the story you tell, and your physical exam findings

diagnosing Long COVID is really no more challenging than diagnosing rheumatoid arthritis most of the time

(I actually find it odd that most people don't realize that what doctors do is use their mind to make a diagnosis on pattern recognition... (that 5 different kinds of arthritis look wildly different to them)... and they use tests to either narrow, confirm, or rule out)