Does the Biden $10,000 forgiveness plan for students require Congressional approval? Why or why not? Do certain laws have Congress exemption?
No. It's pre-authorized by Congress.
He is (ab?)using the 2003 HEROES act, that was passed to help military families during the War on Terror. It has a provision that the Secretary of Education can "waive or modify any statutory or regulatory provision applicable to the federal student loan program" during an emergency. The Covid-19 public health emergency has been extended multiple times and is still officially in effect. QED
Direct justification from the administration:
You have asked whether the HEROES Act authorizes the Secretary to address the financial hardship arising out of the COVID -19 pandemic by reducing or canceling the principal balances of student loans for a broad class of borrowers. We conclude that the Act grants that authority. The plain text of the HEROES Act authorizes the Secretary to “waive or modify any statutory or regulatory provision applicable to” the federal student loan program, 20 U.S.C. § 1098bb(a)(1) (emphasis added), an authority that encompasses provisions applicable to the repayment of the principal balances of loans, provided certain conditions are met. We conclude that targeting relief towards those individuals who suffered financial hardship because of COVID -19 and who otherwise satisfy the requirements of the Act accords with the Act’s requirement that the waiver or modification “be necessary to ensure that” student loan recipients who are “affected” by a national emergency “are not placed in a worse position financially” with respect to their loans as a result.