The reactions are a bit poorly written. While it's true that aqueous H₂CO₃ is produced in this neutralization reaction, the H₂CO₃ rapidly decomposes to yield CO₂(g) and H₂O(l). Writing the product as H₂CO₃(aq) in the net ionic equation is unnecessarily confusing since it portrays the substance as nonionizing yet water-soluble.
In any case, the Na⁺ and the Cl⁻ are the spectator ions here.