The term that does exist, Chinaman, already has its own pejorative sense. It doesn't need that from me.
All I'm saying is that these other words (again, words that I didn't "make up," but also that nobody actually uses) would sound negative too, and are the actual parallels to the term in the parent's example.
By using the name of the country rather than the demonym for its inhabitants, it implies some sort of preference for the country as country, to the degree that a person defines themselves by it, rather than a simple point of history about a person's ethnic heritage, over which the person had no control.
Not that any normal person thinks that there is anything negative with "some sort of preference for the country as country, to the degree that a person defines themselves by it". It's politically quite extreme to see that as "pejorative".
I'm having real trouble coming up with a single country that has the demonym "[Country name]man."
There is a meaningful difference between the name of a country and the term for someone from that country. The second is inherently neutral, because no one controls where they're born. The first connotes that someone defines themselves by their connection to the country as a country (or that the person calling them that sees that as their primary identity, subordinate to the identity of the country itself).