The SEC “curtails first amendment rights” all the time. It’s arguably one of their most effective means of enforcement: an order or agreement to stop lying.

I am not a lawyer, but restricting Musk from being able to speak publicly seems an overly-broad way of restricting him from lying about market-related things, given that the latter is a small subset of his overall speech.

I don’t think it’s likely the SEC would prohibit him from using twitter altogether but I don’t think it’s entirely beyond their ability, either. Especially in the context of a settlement agreement.