There is a test for Covid specific T Cells. Costs about $150. Adaptive Biotechnologies. https://www.t-detect.com/
Maybe given your knowledge you can comment on the test. AB is a credible company. $150 for a test including the on site blood draw seems like something very different than what you are describing.
I don't have time to break that test down today or tomorrow, but I will look at it. Thanks for the tip. It's been a while since I was doing T cell work.