This is factually incorrect. You don't have perhaps protection against infection, nor probably symptomatic disease, but there is working natural immunity, in the form of immune memory and cell based immunity (T lymphocytes). That is far, far more resistant to variants than humoral (antibody based) immunity, mainly because only antibodies neutralizing the S protein are able to prevent infection (so more vulnerable to mutations).
Cell based immunity can't prevent infection, and can not necessarily prevent disease (as in, having fever, cough...), but it is very effective in dampening the effect of infection (either through recruitment of other immune cells, or by killing infected cells). Memory T and B cells generally last quite a lot of years (and with SARS-CoV-2, up to two years at least), so this memory is long-lasting.