For H₂A as a diprotic acid
H₂A + H₂O → HA⁻ + H₃O⁺
And for the second dissociation:
HA⁻ + H₂O → A⁻² + H₃O⁺
Ka of HA⁻ is much lower compared to HA
so second dissociation is slower compared to first.
and already solution contains H₃O⁺ ions from first dissociation so second dissociation becomes much weaker due to common ion effect.
so H₃O⁺ from second dissociation is very less.
so auto-ionization of H₂O has greater impact.
while in first dissociation more H₃O⁺ comes from H₂A
so auto-ionization do not have much impact.