you are right, constitutionally, prisoners are considered Slaves of the State.
I doubt if the word “slave” appears in any criminal law except as a crime to be punished.
Nowhere does any law define convicts as “slaves” of the state.
So the term applied to convicts is simply a colorful metaphor.
Indeed, we are all arguably “slaves” to some passion or other.
As Jesus said (paraphrase): If you commit a sin you are a slave to sin.
Finally, I think the courts have ruled that states cannot, in effect, treat their prisoners like slaves, not certain just where they draw the lines.