If the vaccine killed 1/100 people (again I don’t believe this but it’s the internet) but made the other 99 immune to dying over the 4 years, it would look really good on average even if it was directly responsible for the deaths of 1%.
It's only the case if the vaccine gave everybody slightly higher chances of dying from everything that it could hide in the weeds.
So in this specific example we can see from Table 2 that deaths/1 million are just lower for everything in the vaccinated so it's not the case that it lowered one kind of death drastically at the expense of another.
If you take the vaccine, you have a lower chance of dying over those 4 years. You also have an infinitely higher chance (specifically 1% vs 0%) of dying from the vaccine, but that doesn't change the previous sentence.
But with Covid-19 vaccination wasn't able to eliminate its spread so it mostly is about protecting yourself rather than protecting others.