It’s not like the original tweet wasn’t widely discussed.
If anyone getting paid out of taxpayer funds doesn't grok the Bill of Rights, then their employment is what needs deleting.
By your logic, Elon could tweet Tesla's financial results on twitter during a quiet period before public release "because first amendment". The first amendment doesn't give you carte blanche to break the law without consequence...
If equality before the law were a meaningful concept any longer, the distinction between business accounts with SEC constraints as modifying the 1A might be coherent.
These days the government enjoys the tyranny of selective enforcement (e.g. riots vs. "peaceful protests") to the extent that regarding your point as a fair one is challenging.
If Elon stood on the street corner shouting lies into a megaphone? Sure, maybe there'd be an argument there
People need to think these things through ahead of them getting too far into Godwin's Law territory.
I don't understand the fascination of some sects of the United States with defending such obviously detrimental practices with "well under an extremely loose reading of this amendment it might technically be allowed, and as we all know amendments can't possibly be changed so there's nothing we can do".