Seconding the request for a source. The papers I've found say that SARS-1 survivors have antibodies that react to SARS-CoV-2 but don't neutralize the virus, and thus may not provide immunity.

So far the mRNA vaccines have shown strong effectiveness against the variants, but the others like AZ and the Chinese/Russian vaccines much less so. It's also worth noting that natural immunity is a somewhat random process (more random than the antibodies produced with vaccines) and not everyone develops the same level of protection.