Looking for antibodies wouldn't work, because natural immunity would already have those same antibodies without the need for the vax. Natural immunity produces antibodies to fight all parts of the virus, whereas the vax can only make you produce antibodies to fight to single spike protein the mRNA vax makes your body produce.

Everyone unvaxxed who ever had Covid or had been shed on by people who were vaxxed would have those antibodies. Hence why no test for those specific antibodies has ever been produced. It'd reveal a hole in their system.

As a side note, experimental medicine requires a control group, so a large number of "vaxxed" have never received the real vax but only placebos. The above mentioned test would also reveal that as well.