Trans teacher here, here's no 2 cents. Obviously I am a huge ally, and many of my colleagues are too, but not everyone I work with is. The majority of the trans students that I teach are not out to their parents, are not changed in school software, and importantly, not out to every teacher. It sucks to get deadnamed and misgendered, a lot, I completely understand...but my personal suggestion is to immediately get involved with a queer organization or find some queer friends and get the lowdown on who will be safe to tell. It only takes one transphobic ass of a teacher to "accidentally" out you at parent teacher conferences or in an email. If staying protected from your parents knowing is top priority, find a safe community instead of a blanket coming out.
Was about to type out everything you just did, only less well summarized. Completely agree, you cannot trust your safety to people you don't know. Even if they are people who are supposed to be safe, you can't guarantee that unfortunately.