For a diprotic acid, why does the autoionization of water have a greater impact on the ph at the second equivalence point?

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.