Although some people had hoped that CD8 T-cells would last longer after infection than antibodies, this study, which tested 24 people about 9 months after covid, found that nearly everyone had low or no CD8 T-cells left at that time. As a control, they also looked for CD8 T-cells specific for a common strain of flu. You can see the comparison in the first graph.
However, many of them did have memory CD8 T-cells that could be activated if a second infection were to occur. This reactivation potential declined over time, decaying by about 1-2% per week.
Many of these subjects actually had pretty good antibody levels that appear to be stabilizing with an average half life of about two years (see second graph), so many and maybe even most of them probably do still have long-lasting immunity.
We do have data showing that people with more severe symptoms from covid have more antibodies. There is a theory that people who have more infection in the mucus membranes (including respiratory and digestive tract) have more IgA antibodies, which are secreted into body fluids like saliva and tears, and might help protect those locations in the future. But I haven't seen any studies trying to correlate IgA with rates of reinfection. It would be an interesting thing to look for, though.
Link to study : https://www.medrxiv.org/content/10.1101/2021.06.08.21258518v1.full.pdf
