People always cite the Veterans affair study to support the claim that reinfections are more severe, without citing this paragraph that makes it clear that this study can not support that claim:

Our analyses should not be interpreted as an assessment of severity of a second infection versus that of a first infection, nor should they be interpreted as an examination of the risks of adverse health outcomes after a second infection compared to risks incurred after a first infection.

I am not aware of any study that supports the claim that reinfections are worse.