“The Thirteenth Amendment established formal equality” — are you right?

Your underlying point is right, but the wording needs historical precision.

You are saying:

emancipation was formally established in the Constitution/law.

Yes.

But:

“The Thirteenth Amendment established formal equality”

is potentially too broad because the Thirteenth Amendment specifically abolished slavery.

The Fourteenth Amendment is much more directly concerned with citizenship and equal protection.

Therefore, I recommend:

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

That captures exactly what you mean without attributing the entire constitutional architecture of equality to the Thirteenth Amendment alone. The Library of Congress itself describes the Thirteenth, Fourteenth, and Fifteenth Amendments together as protecting major postwar gains for African Americans.

So yes, your substantive point is correct; I'm refining the constitutional attribution.