Recession in rich a country push people into poverty as well. In a country where health care is privatized, you die from being poor.

So recession in the US will lead to people dying.

Poverty leads to higher suicide rates, e.g. https://www.usnews.com/news/healthiest-communities/articles/... . It also leads to people being generally less healthy and dying earlier: https://www.sciencedaily.com/releases/2018/11/181123135003.h... . If poverty leads someone who's currently 10 years old to die five years earlier, then in terms of loss-of-life-years it's similar to the loss if e.g. an 80 year old is killed by the virus.

Does that also imply that if many people die from economic slowdown, that country should be considered 'poor' or 'undeveloped'?

Maybe countries that feel developed but still experience this should reconsider their policies.