Feat: showDatePicker - Exposed callback when user changes Date Picker Mode - #119116

Exposed a callback when the user switches between entry mode from calendar to input, this way we can store the preferred input method in the application state and open the next date picker with the preferred entry mode already set (using the existing initialEntryMode parameter).

Fixes #113423

Example of callback onDatePickerModeChange

showDatePicker(
  context: context,
  initialDate: DateTime.now(),
  firstDate: DateTime.now(),
  lastDate: DateTime.now(),
  initialEntryMode: datePickerMode,
  onDatePickerModeChange: (mode) {
  setState(() {
    datePickerMode = mode;
  });
  },
)

Screen Recording

CC: @Piinks , @HansMuller

Pre-launch Checklist

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