This is mainly media workers exploiting current events for traffic, even if their content is misleading. We really need to sort out media corruption and incompetence.
Did a quick search of Elon + Twitter. Everything they reported seems factual and tied to things that actually happened? If Twitter does lay off a large amount of people will you admit that Washington Post probably had good sources or continue to be continually skeptical?
I think part of wanting a good media atmosphere is rewarding news sources that are shown to be reliable - and I would argue Washington Post is close to that.
Personal email, obviously. Never discuss anything of this nature on any communication medium that is owned by your employer. There's a reason "Direct Message" labeling overtook "Private Message" in chat apps.
Depending upon how sensitive I’d generally try to avoid written communications in general. It’s easy for even well-meaning friends, current or ex-workers to forward something without thinking it through.