Set originator for codex exec (#4485)

Distinct from the main CLI.

codex-rs/login/src/server.rs

@@ -16,7 +16,7 @@ use base64::Engine;
 use chrono::Utc;
 use codex_core::auth::AuthDotJson;
 use codex_core::auth::get_auth_file;
-use codex_core::default_client::ORIGINATOR;
+use codex_core::default_client::originator;
 use codex_core::token_data::TokenData;
 use codex_core::token_data::parse_id_token;
 use rand::RngCore;
@@ -315,7 +315,7 @@ fn build_authorize_url(
         ("id_token_add_organizations", "true"),
         ("codex_cli_simplified_flow", "true"),
         ("state", state),
-        ("originator", ORIGINATOR.value.as_str()),
+        ("originator", originator().value.as_str()),
     ];
     let qs = query
         .into_iter()