This kind of testing isn't exactly cheap and it is hard to standardize because of all the variables and the fickleness of the process. The one you link is specific to one particular laboratory. These tests also tend to fail a few weeks or months after the infection.

Nor does it actually prove any immunity against disease. You can only assume that these antibodies probe prior contact to the virus and that this prior contact resulted in a robust response. The strength of the immunity cannot be inferred from such titres...

It's expensive, so noone should have the option even if they pay for it? (friend paid about 20€)

It can have false negatives, making people needlessly take a vaccine, so everyone should take the vaccine in the name of equality?

Vaccine certificates neither prove you actually got the vaccine (though highly likely), nor do they prove any immunity against disease (though fairly likely).

With this level of arguments, I can argue noone should be permitted to take the vaccine.

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.

I hope you expect every single vaccine production lab to do control studies on vaccine effectiveness.

Otherwise you're just arguing with double standards trying to console insecurity.