No, they've said in court that he is a White House advisor with no decision-making role (not even at the recently-renamed US DOGE Service, which—despite the public portrayal of him as (originally co-)head of DOGE, he is not formally involved in).
"I signed an order creating the Department of Government Efficiency and put a man named Elon Musk in charge," Trump told an audience of investors and company executives in Miami. [0]
So is Trump lying? Confused? Senile?
And the pushback to Musk by most of his administration didn't take the form of "this guy is just an advisor". They acted as if Musk were in charge, no matter what Trump tells a judge.
[0] https://www.reuters.com/world/us/trump-appears-contradict-wh...
Edit: However the "failure to respond is a resignation" part was Elon and so yeah, maybe your #1 point stands as well.
Musk (1) impersonated a manager to (2) declare a fraudulent employment policy in order to (3) threaten employees and create a hostile working environment with the goal of (4) constructive dismissal.
P.S. Item #1 may not apply depending on on some other court cases, where the Trump administration is refusing to say exactly WTF Musk's role actually is, probably because no matter which mutually-exclusive thing they pick they've still broken the law.