Due to difference in rate of infection, both by spread and risk of contraction. Your UC Davis article does not show otherwise (it is conditioning on aspects of the infection among those already infected and does not measure the risk of being infected - only percent of days you test PCR positive), and there is extensive evidence showing less risk of both among the vaccinated.

https://www.cdc.gov/coronavirus/2019-ncov/science/science-br...

https://jamanetwork.com/journals/jama/fullarticle/2786040

The science around viral dynamics re: viral loads is much more uncertain than this - so I am not saying it is definite that the viral loads are less, only that there is both a mechanism and some evidence to suggest it is either less or quicker to go down (but the evidence here is mixed and it likely wears off).

But nonetheless, the science on transmissibility - even with breakthrough, is more certain.