The login and register pages were near-identical after the previous cleanup,
and both forms repeated the same labelled, icon-prefixed input seven times.
Move the data loading and page shell into auth-landing.tsx (loadAuthLanding +
AuthLandingView) and the input markup into a single AuthField, so the pages
become thin compositions and every field shares one focus, icon and aria
implementation. The numbered section headers collapse into AuthSectionHeader.
No behaviour change.