There are, of course, many ways to measure this, some of which are slightly higher for Germany and some for Mississippi. Many are in the same ballpark, which is pretty crazy to think about. Many of these statistics take into account the taxpayer-funded programs you mentioned.
Broadly speaking, the median Mississippian is about as rich as the median German, with the tradeoff being that the Mississippian has greater access to private goods (e.g. a fishing boat or a big car), whereas the German has greater access to public goods (e.g. socialized insurance or college).
My point is that even "the poor" in America are really quite well off, and not just in historical terms.
Your point is totally and completely wrong. Germany has public benefits that actually matter. Germany's average life expectancy is ahead of Mississippi by *10 years*. Germany ranks as one of the highest in the world in general satisfaction of the people, Mississippi does not.
Why is the median considered "poor"? The true poor in Mississippi are way worse off than those in Germany. If you neglect everything it takes to live a good life like public capital, education, healthcare, time off with family, a retirement, total years on this earth and ignore the insane inequality in Mississippi then sure the median numbers are not that far off.