Function build_public_router 

async fn build_public_router(
    config_db: GCSharedConfigDatabase,
    serve_path: Option<PathBuf>,
    ldap_config: Option<LdapConfigBuilder>,
    default_user: Option<UserID>,
    state: SharedState,
) -> Result<Router, GCHubRestServerError>

Builds the public router: full API with authentication, CORS, and static file serving.