https://covid.cdc.gov/covid-data-tracker/#rates-by-vaccine-status
and then go by age group, you see that the entire "spike" in deaths is made up of people 80+, with most of the rest of the spike made up of people 65-79. (you know, the people who where most likely to die during the winter in the first place). What the data doesn't show is how many of them weren't vaccinated because they were already in a particularly feeble state and maybe their systems weren't strong enough for the vaccine anyway.
If you take those groups out, there is statistically significant increases in mortality for unvaxxed v. vaxxed deaths to show some correlation at younger ages, but at a much smaller magnitude, and it could very well be that there's a stronger correlation to poor health overall and being more likely to die from some other comorbidity than there is a correlation to vaccination status... but that doesn't make for as good of a headline I guess.