This study is using data from 2020 and 2021.
I don’t recall seeing any data showing all cause mortality higher among the vaccinated, although there are various studies showing all cause mortality higher among the unvaccinated (large Hungarian study, UK ONS data, etc.)
There is some data claiming to show higher Covid-specific death rates among the vaccinated, but that’s really only been since 2022 and is typically from countries with extremely high vaccination rates so the unvaccinated population can be easily confounded by things like natural immunity.