I think I've answered your questions, but perhaps an illustration will work to show what I think the issue is, and why I think there is a chance the courts will say that the Secretary of Education lacked authority to forgive the loans.
Here is an example of a law, passed by Congress, explicitly granting authority to the Secretary to forgive student loans.
https://www.law.cornell.edu/uscode/text/20/1087
As you can see by the plain language of the statute, authority is granted to the Secretary, if certain conditions are met, to forgive loans.
Here is what I think the Biden administration is relying on for the current blanket, forgiveness plan.
https://www.law.cornell.edu/uscode/text/20/1098bb
In very general, non-specific language, the Secretary is granted the authority to waive or modify statutory requirements relating to student loans, if certain conditions are met.
I think we can agree that there is a significant difference in the specificity of delegation language in these two laws. The first one is unambiguous. The second, pretty broad and vague.
That's why, I believe, there is an open question as to whether the authority was granted. Now, which way will the courts go on this? No idea.