the data is available here
Age-standardised mortality rates for deaths involving coronavirus (COVID-19) in England by vaccination status, broken down by age group.
www.ons.gov.uk
ehh, vaccines take up to 3 weeks to become effective
Vaccines trick the body into building immunity against infectious diseases without causing the actual disease.
www.betterhealth.vic.gov.au
So it would be a correct procedure to count those vaccines within 21 days as unvaccinated.
Except you can download the data set.
The biggest issue is people misunderstanding the data. For starters, the boosters were only given to the most vulnerable, and there are relatively few vulnerable that didn't take the boosters, so looking at mortality rates is very nuanced and easy to misinterpret.
For example, you already made a critical misunderstanding in regards to why people vaccinated within 3 weeks are not considered to have the full benefits of the vaccine