No, they do not.
Tests show people are antibody and T cell reactive 17+ years after SARS1. This wouldn’t be any different. Antibodies are temporary and then we have our T cells to kick in! Immune systems are great.
Vaccines probably provide years of immunity as well as natural infection judging by SARS1. I had it but got vaccinated because I want to travel and we pretend natural immunity doesn’t exist.
In a study of hospital workers, it showed nearly half of the group didn't have the appropriate t-cells (the more mild or asymptomatic the more likely to not have tcell with the needed spike).
If you have the tcells yes you should be covered for most/all variants studies show. There so much not known. The studies are so small and short in length as data collection stated only a year ago.