So yes, economies relying on slave labor can outcompete our economies in sectors where masses of low skilled labor are required (because of the lower price), but once these economies move up and require highly skilled labor they'll usually get into trouble.
It need not be codified into law. It can be accomplished by way of a severe wealth disparity, a glass ceiling, stratification of housing, stratification of education, etc., and a legal system that treats upper class people significantly better than lower class ones. Everyone is technically a citizen subject to the same laws but in practice a different set of laws apply to you based on your wealth, occupation, connections, and what neighborhood you live in.
Edit: yes the US is a bit like this, but you can take it a lot further.
So glad the US isn't like that...
If you're a semi-meritocratic secular authoritarian state like China that isn't too difficult. If you're a religious conservative authoritarian state, that's close to impossible. Knowledge workers are willing to live with authoritarianism as long as it doesn't overly restrict their personal lives and interactions, and religious conservatism is all about restricting personal lives and interactions.