Can you cite Smith for that proposition and then apply it to emancipation?

Yes — with a qualification.

Smith gives you the conceptual framework, not specifically the historical evidence about emancipation.

His article explicitly distinguishes:

legal citizenship

from

lived citizenship, including social recognition and social standing.

So you could use Smith to establish your analytical distinction:

Rogers M. Smith (2022) distinguishes legal citizenship from lived citizenship, arguing that equal citizenship involves not only uniform legal rights and duties but also sufficient social, political, and economic standing for people to be recognized as civic equals.

Then apply it historically:

This distinction is relevant to the post-emancipation United States, where formerly enslaved African Americans acquired legal freedom while continuing to face social hostility, segregation, and racial violence.

That is methodologically sound because you are doing two separate things:

Smith → provides the conceptual distinction.

Library of Congress / historical scholarship → provides the historical evidence.

You should not write:

“Smith proves that formerly enslaved people were not socially equal after emancipation.”

He isn't making that specific historical claim in this article.