I'd have to look into it again but I'm fairly certain student debt (not just any debt) is one of those things that the president has huge power over. Similar to drug scheduling. Nancy isn't credible so I'd take anything she says w/a grain of salt.
I looked into it awhile ago and came to the conclusion he cant.I will look into again later but I remember they were trying so many sketchy ways to justify it that if republicans were doing the same for an EO they wanted I would call bullshit.IIRC first they were trying to use a 1960s law for justification now they are trying to use a 2003 law.
That said I do support it and give Biden credit for fulfilling at least 1 major progressive promise.