The antibodies are only detectable for a short while, much shorter than immunity. Your body isn't full of antibodies to every microbe that has attacked you but the information is stored in your immune system (T and B cells, etc.) so antibodies can be made when a familiar enemy is detected. Therefore, you can have immunity with not antibodies detected. Funny how they don't make that clear, right? The T cell tests for Covid immunity have been around for a while but discouraged because it was feared people would refuse to take the fake vaccinations. There is one available in the US