Death certificates are not in VAERS. That’s not what the system is used for. VAERS records adverse events that happen within a specified time of receiving a vaccine. If you get a shingles vaccine today and get hit by a car tomorrow, the death is recorded - by law - in VAERS.
To cut-and-paste your own quote:
Why do they keep stating on official government documents (under penalty of law, loss of medical license, loss of career, potential prison time, etc.) that it was natural causes consistent with the person’s individual medical history?
Prove it.
On a case-by-case basis.
https://vaers.hhs.gov/docs/VAERS_Table_of_Reportable_Events_Following_Vaccination.pdf
I don't see "getting hit by a car" in there.