idk about folks using #Mastodon in English, but on my Spanish UI, the word "private" (well, "privado") does NOT show up in the posting setting that is marked by an "@".
It says "only show to mentioned users."
That's because it IS NOT a private messaging system.
Mastodon DOES NOT HAVE a private message system.
Do not expect it to work as one!
It is SOLELY a way to keep your conversation from cluttering unrelated people's feeds.
It is not designed for #privacy
(I'm seeing people say "it's so weird that when you @-mention someone in a private message, they can see it," which comes from the fundamental misunderstanding that it's a private message system and not a @'d-people-only setting. Once you've @'d them, they're in!)