I don't have time to explain to you the intricacies of antibody testing. However, it is much more difficult than to standardize on what antigens and what titres to pick and how to correlate that for a "positive" result. Testing for neutralizing antibodies is even harder, because it involves isolating the antibodies and testing them against live virus particles and a cell culture.
And yes, standardizing such testing, as complicated and expensive as it is, across all the relevant labs across the country would be a bureaucratic nightmare.
I'm not going to engage with your bullshit about doctors faking vaccinations.