[dialogs] Moving non appearance API to private header
[dialogs] Moving non appearance API to private header

* Issues
b/133006455, b/148572399

PiperOrigin-RevId: 302032495

material-components/material-components-ios,material-components/material-components-ios,material-components/material-components-ios,material-components/material-components-ios,material-components/material-components-ios