Why can you apply Smith to post-emancipation America?

Because there are three levels:

Level 1 — Smith's conceptual distinction

legal citizenship is not the lived citizenship

Level 2 — Smith's American case

Smith examines this distinction in relation to the United States.

Level 3 — Your historical application

This distinction helps explain the difference between the legal freedom established for formerly enslaved African Americans and their subsequent social, political, and economic position.

So yes, you can make the application.

You are not pretending Smith said your exact sentence.

You are saying:

“Smith gives me an analytical distinction, and I apply that distinction to my historical evidence.”

That is entirely normal scholarly reasoning.