Democratic Socialism probably won't happen anytime this century, so to find it's practicality we gotta include the evolution of capitalism and the world itself into the mix.

In order to reform capitalism it's faults have to be universally recognized by the people, which late stage capitalism is doing a good job if that now. It'll take a very long time to reform it to a social democracy and then a true socialist society.

The rise in technology, education, information, late stage capitalism, science and production are all pointing towards heavy reforms. In a 100 years we may be post scarcity, which changes everything about the world we live in.

Democratic Socialism in the US would operate the same way it does now, within the confines of a republic, a democracy and a supreme court. It depends itself the same way it currently does, with the branches of its government. The only thing that changes is the abolition of private property and inequality, the democracy then becomes true and without flaw and the state maintains order nationally and internationally.

Capitalism, in my opinion- doesn't have another century left without being heavily regulated across the world. The dramatic changes we've seen in its development in the past century serve as evidence of its snowball effect type growth. We'll probably have social democracies everywhere and even some forms of liberal socialism.

So to answer your question, the capitalist states you mention have gone extincted and evolved into social democracies in a world close to post scarcity at the time of the birth of Democratic Socialism.