Elections are not statistical tests. Number of people dead are not statistical tests. You said "When we get into "total population" statistics, we kinda leave the realm of statistics lol." That is false. There are many questions that statistics is best suited to answer even if an entire population has been surveyed. Often the term population is poorly defined, and is much wider than the simple base case.

In the case of J&J blood clots, there's billions of additional people who could take the J&J vaccine. 15/21 million people who took he J&J vaccine got blood clots. But if you want to know what percentage of "people who take the J&J vaccine get blood clots" that's not the same thing. The population includes an infinite number of people.