Is моє correct, or does it sound odd to a native speaker? I remember there being a problem with Я шукаю мій багаж.
I'd use «своє» in this sentence. Maybe it's worth reporting it.
It sounds odd to a native speaker.
I don't know why the creators of this course decided to use the "repeating" possessive pronoun (Я .. моє, Ти ... твоє) as the default (свій/своя/своє/свої are accepted as alternatives). Maybe they decided it would be less confusing to the learner.