It's a so called dark post. A promoted Tweet that's not published to the profile, but only distributed to the target audience. It still has an URL and can be manually shared, but it's neither indexed nor on the account page.
I had no idea this existed. So this is something that goes through Twitter ads? I'm assuming so since that's what the source suggests. That's really interesting. The only way I found it was that the id was referenced by replies that were searchable but I didn't see the ID itself.
Yes. Twitter calls them „Promoted-Only Tweets“.
Apple (ab)used them a lot in the past. They created promoted-only replies to notify people when the event started and everyone felt special by getting personally notified and retweeted it. Apple spent $0.