I'll say this for maybe the 30th time (I'm a parent, so I'm cool with that: eventually it'll sink in.)
VAERS reports ALL the bad stuff that happened in the year after someone got the vaccine. So to understand those numbers, you have to ask yourself, "Who got the vaccine first?" and the answer is, the elderly, and people with underlying health conditions. So, the next question is, "How many of a similarly aged cohort die each year, regardless of their vaccine status?"
In 2020, a bit more than 58 million people age 65 and up got the Covid vaccine (approximately 95% of that age demographic). Assuming completely normal mortality rates for people 65+, you'd expect well over a million people of that group to die in the next year, predominantly from heart disease or cancer. So, 10,000 people dying after getting the Covid shot isn't news, it's just statistics. To prove your case, you'd have to find out the death rates in that year of the 5% who didn't get the shot.
What you're looking for is a statistic of excess mortality associated with Covid vaccination. You don't have the data to back that up, but there is a good deal of documentation of excess mortality from active Covid infection.