(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.