Failed to give a bunch of allegedly El Salvadoran immigrants/migrants a hearing to contest their deportation (as required by the Constitution), and then ignore a court order to return those folks to US soil while they were in transit to El Salvador.

This was a blatant violation of habeas corpus.

No, it wasn't. Habeas corpus is a limitation on unjust detention - the government can't imprison you without giving you at least one opportunity to get into court and have a judge see you and hear what's going on.

Deportation is a civil matter. The government certainly denied them due process, but it wasn't a violation of habeas corpus, because it was a civil violation.

The federal government is found to have violated civil laws, even the constitution, all the time. I don't think there's been an Administration that hasn't unanimously lost a case at the SCOTUS for violating a statute or the Constitution in my lifetime. Every Administration has instances where they stretch a legal claim or statutory authority to the breaking point, and get called out for doing it. Even for denying parties due process by refusing to give them access to the courts (as happened during the Obama administration):

https://supreme.justia.com/cases/federal/us/566/12...

Where the Administration did do something unprecedented and wrong was in trying to front-run the judge's order (in their reading) to create facts on the ground that couldn't be undone. But after that, they've been complying with the orders not to deport other folks under the Act while the litigation over its availability is ongoing.

They're 100% wrong in claiming they have this power....but there's a process for resolving disputes over o'erweening Executive interpretations of statutes, and it's playing out.