In Hungarian it’s the same with “home” in particular. You say “I’m home.”. In Hungarian, I too say the exact same thing: “Otthon vagyok” (I’m home).
Your other two example works the same, you won’t say in Hungarian “I’m school” (Iskola vagyok (it means I am literally a school)). But you say “IskoláBAN vagyok” (I’m at school) or “PostÁN vagyok” (I’m at the post office. Notice the suffix in this case is completely different, but that’s another story of Hungarian)