> I've heard people tell me that when COVID started the hospitals started marking everyone who died as having COVID regardless of what the real cause was.

From what I've heard, it went both ways, depending on the point in time. E.g. Poland had an election coming up mid-pandemic, and around that period, many people believed the government is underreporting COVID deaths, by making doctors classify them as caused by any of the comorbidities present in the deceased (and past certain age, pretty much everyone had some comorbidity, e.g. a weak cardiovascular system, or cancer).

COVID statistics were always heavily politicized. I think the most reliable way of getting to the truth was, and still is, looking at the excess death counts (i.e. how many more people died in a given month over the average of deaths in that month in last few pre-pandemic years).