35,000 people died in the year after they received Covid vaccinations, when the majority of the first round of vaccinations were given to elderly or otherwise at risk people? That's a correlation. Consider that the normal mortality rate in the US for people over 85 in a given year is around 10%; for people over 80, around 6%; over 75, around 4% (this is 2022, AFTER the Covid vaccine). You could as easily say that all those people died after wearing the color blue. In 2010, before Covid and its vaccines, the annual mortality rate for people over 65 (aggregated) was about 44%. If I were going to leap to a conclusion like a science and math-ignorant person, I would say that the Covid vaccination reduced the death rate based on that data.
We KNOW that it reduced the Covid death rate: that's been well-attested. Any other correlation that you want to claim causality for, you'll have to prove. VAERS is just a list of ALL THE BAD STUFF people experienced in the year after they got their shots, not a list of things directly caused by the shot.