>Words have objective meanings

Even if you were right about that, which you're not, but it's actually funnier if you are, you'd be wrong about the argument at hand.

Wages, per both Merriam-Webster and Cambridge (which, hint is why you're wrong about the objective definition thing. Why would we need multiple disagreeing dictionaries if words had objective definitions?), are paid to employees based on a contractual obligation.

Prisoners are not employees and are not contractually obligated to participate in work. Prisoners are legally (not contractually) required to complete work (regardless of being employed or not), and can (and do) face punishment for not completing compulsory work.

The reason that you are not seeing people being sentenced "to labor" is that there is no need to sentence someone "to labor" because the laboring is already included in their sentence as a part of their terms of commitment as outlined in the policies of the various prisons as allowed by the 13th amendment.

No court has to specify that the convicted can be compelled to slavery because that specification is inherent in the conviction.

Source: Have been a prisoner.