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.

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?

Yeah... but the FBI doesn't need to write to Congress every time it decides to make an arrest. Congress delegates broad powers to the executive branch and in this case my understanding is that there were relatively few carveouts limiting what could be done with these loans. What I'm asking about is what specifically did the court reference when they said that this action was an overstepping of the branch's authority?

It was authorized by congress, specifically the heroes act. It gave the executive branch the power to "waive or modify loans" in reponse to a national emergency, and cornavirus was declared one. The law passed by congress explicitly gives Biden the power to do this. It'd a terrible ruling by the court. Not to mention the suing parties have no standing to begin with, and the suit never should have even gone forward on that basis in the first place.