“What citizenship would entail”

Entail here means:

involve, require, or include as its implications.

So:

“what citizenship would entail”

means:

What rights, duties, status, protections, and forms of participation should citizenship provide?

For formerly enslaved people, the question could include:

• What political rights should they possess?
• Could they vote?
• Could they participate equally in public life?
• What legal protections should they receive?
• Could they own property?
• Could they make contracts?
• Could they participate as equal members of society?

So when I said:

Formerly enslaved people had to struggle over what citizenship would entail

I meant:

They had to struggle over what their new status as citizens should actually mean in terms of rights, protections, participation, and social standing.