> None of these articles support the claim that "death rates are the same in fully vaccinated vs un/partially vaccinated populations". Probably because no such literature exists.

The documents show that the placebo arms were terminated prematurely and the fact that there is agreement that they are still needed.

Here is Moderna[1]. If you look at Table 19,

           Vaccine        Placebo
    Death* 4/15184 (<0.1) 4/15165 (<0.1)

Here is Pfizer[2]. If you look at Table 14,

           Vaccine       Placebo
    Deaths 2/21621 (0.0) 4/21631 (0.0) 

Locating relevant information for other vaccines is left as an exercise for the readers.

[1]: https://www.fda.gov/media/144434/download

[2]: https://www.fda.gov/media/144245/download