I Transferred a Pokemon into home twice and checked the mobile version and I don't see the mystery gift. Why is that?
The Mystery Gift is available at 5pm in Pacific Daylight Time, 8pm in Eastern Standard Time, and 11Pm British Summer Time. Since those times haven't come yet on June 29th, the gift isn't available. Once the event starts, then transfer your pokémon to Home and the mystery gift should appear. Hope I helped!
The reason you cannot get Shiny Zeraora is because it becomes available later today. Specifically, it is available at 5pm PDT, meaning that is can't be obtained yet. Like I stated, at 5pm PDT, the Zeraora can be claimed.
I hope I helped!
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