Congress should just adjourn for four years - it’s not like they’re going to do anything, apparently.
What
can they do? Whatever laws they might introduce, interpreting and executing the law is now the sole province of the executive branch, and that branch is not itself subject to legal review. If they write some law or other that the president dislikes, he can just refuse to implement it, at least as it pertains to the federal government.
That's not true. At least, not yet. You can't criminally investigate Trump. But it stops at Trump. Also, Trump isn't the Government. You sue the government. Legal standing and ability to sue should still exist. But one needs to be able to say they've been harmed... and that is what Musk seems to be covering up.
That is not what Trump's executive branch has actually said. If that is true in some abstract philosophical sense, it is not how the federal government is functioning at present. There are quite a few lawsuits circulating, yes. But Congress cannot sue, except as individuals. Standing is an issue, as you note, as is sovereign immunity.
I'm pretty certain Congress can sue. They won't, but they can. Trump isn't the Government. So lawsuits can still happen, but in order to have a lawsuit, the person suing needs to have legal standing in a case. And to have legal standing, you need to demonstrate you have a claim that you can justify with regress. That last part would be the tricky part if Musk able to do all of this in secret, because you can't sue for a wrong you don't even know happened.
And whatever protects Trump, doesn't protect anyone else in the Executive Branch.