I have seen very little discussion or information in the popular press about the reliability, poor or otherwise, of the so-called antibody tests. These are the tests which look at the antibodies existing in someone's plasma, and allow a possible conclusion that antibodies which react to SARS-Cov-2 indicate prior exposure to the virus. Most, if not all of these tests were given temporary approval for sale by the FDA because of the pandemic emergency. Most were not at all accurate, and some resulted in false positive results as often as 40% of the time!
Usually, the FDA requires an elaborate validation process for medical tests like these before they can be sold in the US. Basically they require the test manufacturer to show data that establish the test’s accuracy and inaccuracy, and they have to establish how many false positives and false negatives the test sees. Once that data is known, the validation process further requires the manufacturer to modify the test to optimize results, to the extent that they meet existing standards already established by other approved tests on the market. Until this validation process is done, all bets on test accuracy or reliability are off.
Very recently, it does seem that some antibody tests might have been properly validated, but I’m only guessing based on the wording of articles in the popular press. I haven’t looked in the scientific literature about what antibody tests have been successfully validated and approved. Without the pandemic, these type of reports would not result in a scientific publication.