Your observation is actually correct. The Cleveland Clinic paper showed more vaccines —> more infections.
This study found that not being “up-to-date” on COVID-19 vaccination, using the current CDC definition, was associated with a lower risk of COVID-19 than being “up-to-date”, while the XBB lineages were the dominant circulating strains of SARS-CoV-2.
They have two papers to show this:
https://academic.oup.com/ofid/article/10/6/ofad209/7131292?login=false?
https://www.medrxiv.org/content/10.1101/2023.06.09.23290893v1.full#T2
