I’m sorry, but what? Biden v. Nebraska was also about the HEA of 1965.

From the SCOTUS opinion on Biden v. Nebraska:

Title IV of the Higher Education Act of 1965 (Education Act) governs federal financial aid mechanisms, including student loans. 20 U. S. C. §1070(a). The Act authorizes the Secretary of Education to cancel or reduce loans in certain limited circumstances.

The Secretary may cancel a set amount of loans held by some public servants, see §§1078–10, 1087j, 1087ee. He may also forgive the loans of borrowers who have died or become “permanently and totally disabled,” §1087(a)(1); borrowers who are bankrupt, §1087(b); and borrowers whose schools falsely certify them, close down, or fail to pay lenders. §1087(c).

That doesn’t apply to any of these 804k people.

The Biden v. Nebraska opinion also says, while the DOE Secretary has the ability to modify provisions of the HEA of 1965, sweeping forgiveness measures are outside of the legal scope of the definition of “modify” granted by Congress.

Roberts also argued that the HEROES Act authorized the secretary of education to waive or modify student loan provisions but did not authorize the cancellation of student debt:[9]

The Secretary’s comprehensive debt cancellation plan cannot fairly be called a waiver—it not only nullifies existing provisions, but augments and expands them dramatically. It cannot be mere modification, because it constitutes ‘effectively the introduction of a whole new regime.’ MCI, 512 U. S., at 234. And it cannot be some combination of the two, because when the Secretary seeks to add to existing law, the fact that he has ‘waived’ certain provisions does not give him a free pass to avoid the limits inherent in the power to ‘modify.’ However broad the meaning of ‘waive or modify,’ that language cannot authorize the kind of exhaustive rewriting of the statute that has taken place here.

It doesn’t matter that the scope is smaller. It matters that the DOE does not have the authority.