Nope, it doesn't say what you claim. As far as "vaxxed having greater infections," it actually says ....
The rate of death within 28 days or within 60 days of a positive COVID-19 test increases with age, and again is substantially greater in unvaccinated individuals compared to fully vaccinated individuals.
.... which is exactly what I showed you with the math you don't understand.
As far as vaxxed dealing with more "reinfections," the word, "reinfection," appears only once in that report and it's not in relation to vaxxed or unvaxxed specifically....
Please note that from 31 January 2022, UKHSA moved all COVID-19 case reporting in England to use a new episode-based definition which includes possible reinfections. Each infection episode is counted separately if there are at least 91 days between positive test results. Each infection episode begins with the earliest positive specimen date. Further information can be found on the UK COVID-19 dashboard.
So now I see not only can't you do math but you can't do reading comprehension either.