This is an advantage of the vaccine. Where the virus itself causes infection that seems to lower T-cells, the vaccine does not contain the virus.Maybe?
I will go with the experts and the evidence.
The vaccine not only provides antibodies to fight infection but it increases T-cells where as natural infection has the potential to lower T-cells.
"T cell counts are reduced significantly in COVID-19 patients, and the surviving T cells appear functionally exhausted. "
We know the vaccine is effective not only in helping fight off infection but also in recovery from infection. But we do not know how effective the current vaccines will be against future varients.
Pfizer/BioNTech and Moderna vaccines induce T-cell immunity against SARS-CoV-2
Reduction and Functional Exhaustion of T Cells in Patients With Coronavirus Disease 2019 (COVID-19)