The bulls stopped binding anyone long before their reasoning did. Protestant powers rejected papal authority over the Atlantic in the sixteenth century and took the lands anyway, and by the eighteenth century no European state grounded a colonial claim on a papal grant. What survived was the underlying rule: that the first Christian or European power to reach a territory acquired title against all other such powers, and that the people already there retained only a right of occupancy.
In the United States that rule entered the common law by name. In Johnson v. M'Intosh in 1823 the Supreme Court, in an opinion by Chief Justice John Marshall, held that discovery gave title to the government by whose subjects the discovery was made, and that the rights of the original inhabitants were thereby diminished to a right of occupancy which only the discovering sovereign could extinguish. Marshall traced the principle through the charters and the earlier European practice the bulls had shaped. The decision has never been overruled, and the Court cited the discovery doctrine again as recently as 2005.
That is why the 2023 statement from the Holy See, which repudiated the concepts the bulls carried, changes the Church's position without changing anyone's land title. The instrument and the doctrine parted company centuries ago, and they now sit in different jurisdictions.
Sources Discovering Indigenous Lands: The Doctrine of Discovery in the English ColoniesRobert J. Miller, Jacinta Ruru, Larissa Behrendt and Tracey Lindberg with Joint Statement of the Dicasteries for Culture and Education and for Promoting Integral Human Development on the Doctrine of DiscoveryHoly See