Rule? Maybe.
Asking itself is one thing. Unethical at worst. But how does a company interpret an ask from a government official without a perceived threat? Therefore, elected officials should have clear ethics guidelines in place.
The moment the ask comes with clear pressure or threats that could only come with the status of office held, should be subject to the rules and ethics of the governing body itself (i.e. censure or impeachment by the Senate).
What ethical standard would you suggest should govern whether Harris can ask X to take down the fake tweets about her injuring a child in a DUI accident?