There have been rigorous studies that correlate the specific vaccine with the specific desired outcome of immunity.
You probably can't understand (and don't want to) why that is not the case for people who got infected at some unknown random point in the past and with an unknown, random variant of the Virus. And I don't care to explain it to you.
And you probably also don't want to understand why those lab tests aren't designed, regulated or approved as a proof of immunity. To be rigorous enough, probably every single lab would have to do control studies to find out if their tests predict immunity against reinfection.
You probably can't understand (and don't want to) why that is not the case for people who got infected at some unknown random point in the past and with an unknown, random variant of the Virus. And I don't care to explain it to you.
And you probably also don't want to understand why those lab tests aren't designed, regulated or approved as a proof of immunity. To be rigorous enough, probably every single lab would have to do control studies to find out if their tests predict immunity against reinfection.