Set originator for codex exec (#4485)

Distinct from the main CLI.

codex-rs/exec/src/lib.rs

@@ -38,9 +38,14 @@ use tracing_subscriber::prelude::*;
 use crate::cli::Command as ExecCommand;
 use crate::event_processor::CodexStatus;
 use crate::event_processor::EventProcessor;
+use codex_core::default_client::set_default_originator;
 use codex_core::find_conversation_path_by_id_str;
 
 pub async fn run_main(cli: Cli, codex_linux_sandbox_exe: Option<PathBuf>) -> anyhow::Result<()> {
+    if let Err(err) = set_default_originator("codex_exec") {
+        tracing::warn!(?err, "Failed to set codex exec originator override {err:?}");
+    }
+
     let Cli {
         command,
         images,