This would make quite a few Congressional hearings unconstitutional. For example: https://www.nbcnews.com/tech/tech-news/4-tech-industry-titan...
It'd probably also apply to the President saying "lock her up" about a private citizen. Is that unconstitutional pressure from an elected official?
> What does that even mean, for the US Government to have a right to speak without fear of action being taken against it by the US Government?
It means stuff like this: https://en.wikipedia.org/wiki/Speech_or_Debate_Clause
Well, maybe, if you ignore the Constitutional carte blanche for Congressional proceedings of the Article I Speech and Debate Clause.
It's quite common for elected officials to criticize private citizens and businesses. To be concrete: Ted Cruz (and a bunch of others) publicly pressured the NFL over players kneeling at games, in a clear attempt to suppress First Amendment expression by said players, without any hint of consequences.
They can criticize all they like.
What they can't do is order the political speech of citizens be censored.
The First Amendment distinction here being what, exactly? The President can chant "lock her up" but it's a violation if their FBI director does it?
[citation needed]
The IRS disagrees, but obviously different legal contexts have different definitions, but I am aware of none supporting the distinction you are trying to make.
In Garcetti v. Ceballos, the Supreme Court held “that when public employees make statements pursuant to their official duties, the employees are not speaking as citizens for First Amendment purposes, and the Constitution does not insulate their communications from employer discipline.”
Obviously, speech and debate clause controls for Federal Congress members.
