“Formal legal equality does not exhaust the practical realization of equality”

“exhaust” means “fully encompass.”

Emancipation established formal legal equality, but this did not automatically produce social equality between formerly enslaved Black people and white Americans.

That is much closer to what you are actually trying to say.

And here we need to be careful about one historical detail:

The Thirteenth Amendment itself abolished slavery; it did not by itself establish all the constitutional dimensions of equal citizenship.

The Reconstruction Amendments worked together:

13th Amendment — abolished slavery;

14th Amendment — citizenship and equal protection;

15th Amendment — voting rights for African American men.

The Library of Congress explicitly distinguishes these functions.

So if your sentence says:

“The Thirteenth Amendment established formal equality”

a very careful historian might object that the Fourteenth Amendment is the more direct constitutional source for equal citizenship and equal protection.

Your safer formulation is:

Emancipation and the Reconstruction constitutional amendments established the formal legal foundations of freedom and equality for formerly enslaved African Americans.