(a) Do you call any case where someone turns out to be wrong "false messaging"? Their prior knowledge led them to believe (wrongly, but it seems to me, quite honestly) that non-N95 masks would not be effective, and they didn't have evidence to the contrary, and they
very openly explained that their fear is healthcare providers not having masks, which was 100% a sincere worry any official worth their salt would have.
(b) A tweet only has so much room to explain things. There's a reason websites in general, official CDC recommendations in particular, and the news media exist. If the only source of information you get your news from for several weeks amidst a pandemic is Twitter, and the tweet turns out to be lacking some info, the problem isn't the source you're reading.
(c) Even if you establish there was "false messaging from the surgeon general on Twitter" (which you haven't due to the reasons above), it's quite a goalpost move from "the CDC was being deceptive/manipulative". Especially when the the surgeon general was picked by the president and specifically not the NIH authority figure that the nation was looking up to 24/7.