Your understanding is correct. PCR tests can only tell if you are currently infected. (Or at least have been so recently infected that enough remnant mRNA is still lingering in your body to be detectable.)

Antibody tests can determine whether someone was infected previously, and I have heard that there are some that look for antibodies that are associated with infection but not vaccination. I don't know anything more about them than that, but maybe that could provide a thread to help start searching if you are interested in finding out more about them.