Studies are looking for vaccine effectiveness, not vaccine issues. If there are issues, that would require getting the spreadsheets and looking at when people got sick after taking vaccines, and seeing if there is a pattern with factors like age, comorbidities, time after vaccination of infection.
From figure 2 in the link you posted, partial vaccination has issues. If people are getting sick after the first does or shortly after the second dose in a narrow date range, then would be a cause for concern. AFAIK no one has presented the data on when people are getting sick during and after vaccination. Any doctor raising these issues risks censorship like Dr. Charles Hoffe.
I am not following what you are saying in your critique of her post. My understanding is this.
You will have a chart of hospitalizations or deaths from the CDC. The pair breakdown is vaccinated and unvaccinated. However because of how they define who counts as unvaccinated (it includes people vaccinated within 2 weeks) some of the hospitalized or deaths in the “unvaccinated” column are actually vaccinated