The home tests are antigen tests. They contain some of the antibodies the immune system creates. The antibodies bind to the spike protein to create the mark in the test kits.
To test if you have natural immunity, it must be done the other way round, antibodies in your blood must bind to something that resembles spike proteins - an antibody (or serum) test. There are also tests that can detect if you have t cell immunity. Both are lab tests.
Do you have to put a swab up your nose or just spit on something?
Depends on the antigen test and how the FDA has approved it. Serum tests need blood.
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