Last I heard the Biden administration is leaving it up to the CDC whether to appeal or not.

The fear is that if the case goes to the Supreme Court and the administration loses, then that precedent wil prevent the CDC from ever being able to impose any kind of mandates again on any issue.

Of course they are correct to fear SCOTUS with its conservative majority. Which was my argument in this article. With conservative judges throughout the judicial system, unreasonable laws will be upheld while anything the Democrats pass will be struck down.