The category isn't really the important part here. I don't care about definitions. Instead, I care about the actual real world effect. Th semantics is not important here.
So, no, I would not find it unusual for a law to have the real world effect of preventing the government from hiring a repair company that discriminates on the basis of race.
And whether or not those laws reflect the definitions of words, as defined by some webster dictionary here, is not the important part of the debate about whether we ought or ought not have certain laws.
Instead what matters is the actual effect of those laws.
It is not the wrong category though, because this is a well established definition within the law that everyone in that community understands.
Instead, the problem is that your intuition is different than the well established definition of these categories, as according to what the court system has established.
> to shoehorn them
It is not shoehorning though. It is an established and understood concept that courts understand. Instead, it is your personal intuition that is wrong regarding a law that is well understood by the court system.
Would you find it unusual or outlandish for a law to place contractors employed by the government in the category of "entities receiving financial assistance from the government"?