In this context, the executive branch is literally saying they don’t want to do their job

That seems... tenuous? This strikes me as a traffic-ticket kind of situation where there are multiple equally legal courses of action that the official can choose to apply. If the department is charged with enforcing the terms of a loan contract and that contract contains a cancellation clause, on what basis is the court ruling that invoking cancellation is any different from acceptable actions like invoking a lien?

No this isn't really it in this case. There was a law passed by congress called the heroes act. It explicitly gave the power to the executive branch to "waive or modify" loans in response to national emergencies. Corona virus pandemic was legally declared a national emergency, so Biden invoked the law to waive and modify the loans. The supreme court is really out here in left field, bending over backwards as to why the executive branch can't use the heroes law in this way. John Roberts wrote some ridiculous stuff about how "waive" and "cancel" aren't the same or something. The conservatives claim to be "textualists" but this is a false front, they just claim whatever partisan republican priority at the time they feel like.