> Does the United States actually practice slavery in the prison system in any fashion?
Yes, and it is precisely the reason the US is one of the few eligible countries not to have ratified the main current treaty against slavery, the ILO Forced Labor Convention.
> My understanding is that work is optional
Prison labor is generally mandatory for able-bodied prisoners in the federal system, and this is true in some state systems as well.
> Is any US State or Federal prison running cotton plantations in Georgia with forced, uncompensated labor?
Historically, slavery has often had compensation, and, yes, there are literally forced labor prison farms in the USA, such as the Mississippi State Penitentiary, aka “Parchman Farm”.
There have been some reforms since the origins of the penal slavery system in the US, in which the government involved literally rented convicted out to private businesses, but it remains a system of slavery, often involving a public/private partnership for profit.