As far as antibodies testing goes then I was sent a home test kit as one of 200,000 randomly selected people. I tested positive for both the long lasting antibodies and the ones that only stay in the body for a few weeks. I had my 2nd jab 3 weeks before the test so I guess that is why I had some of the shorter lived antibodies.
In LA County our daughter has been randomly selected to have an antibodies test and should get her home test kit this week. This test is only looking for the type of antibodies that show you have had Covid, which are different from the ones induced by a vaccine. She has had 2 jabs of Pfizer and has not, to her knowledge, had Covid so expects her test results to come back negative. LA County know how many folks have been vaccinated, but are wanting to get an estimate of how many folks have antibodies without having had a vaccine and if they have had Covid how well is their protection against future infection holding up.