13th amendment doesn't apply to the government?

“The phrase “involuntary servitude” was an attempt to prevent nominally free citizens from being trapped by a plutocrat with a sharp lawyer.”
But not a government open to “interpretation”?
In other words, what is the fundamental difference, in practice, between these illegal practices and the legal draft?

The others mainly affect relationships between one private entity and another private entity, in the context of the civilian labor market in a peacetime economy.

The draft affects relationships between the individual and the society, in the context of a national emergency.

Then, mbh, as I read it, it seems to me that the government–a declared public institution–cannot have slaves. Only private entities (inc corporations, I assume) may have slaves.
Still seems to me to be exactly what the title of this thread is: the amendement doesn’t apply to the government. They are, to put it bluntly, above the law in this case.