Public statements by your CEO can easily impact your work. Twitter might have a trivial and lighthearted feel, but that doesn't detract. Eg, when Musk tweeted he was taking Tesla public, it was probably very disruptive, regardless of the medium. I think one of the lessons of the last few years has been that things people say on Twitter do, in fact, matter a great deal.

ETA: I had a brain fart and thought we were talking about Tesla, but the example is illustrative nonetheless.