Here's how it works:
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The system is composed of a reader, a database and the digital ID on your iPhone or Apple Watch.
1. The user taps their device on the terminal.
2. The terminal sends your device the information it's asking for.
3. The user sees what information they're granting:
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4. The user authenticates themselves with Face ID and grants sending that information.
5. The terminal receives the authorization, which then contacts the state database with the authorization which sends it.
At no point are you giving your device to anybody. There's nothing on screen that identifies you, so showing it serves no purpose either.