fix: prevent codex-backend from stealing originator (#22533)

## Why

Remote control starts by letting `codex-backend` initialize against the
app-server as an infrastructure health/proxy client before the real
remote client connects. App-server initialization also sets the
process-wide `originator` from `client_info.name`, so `codex-backend`
could become the sticky originator for later model/API requests even
after the real client initialized.

## What changed

- Treat `codex-backend` as a non-originating initialize client,
alongside the existing `codex_app_server_daemon` probe client.
- Preserve normal per-connection initialize behavior, including session
metadata and initialize analytics.
- Add regression coverage that verifies `codex-backend` initialize does
not replace the default originator.

## Testing

- `cargo test -p codex-app-server --test all
initialize_codex_backend_does_not_override_originator`

codex-rs/app-server/tests/suite/v2/initialize.rs

@@ -89,6 +89,33 @@ async fn initialize_probe_does_not_override_originator() -> Result<()> {
     Ok(())
 }
 
+#[tokio::test]
+async fn initialize_codex_backend_does_not_override_originator() -> Result<()> {
+    let responses = Vec::new();
+    let server = create_mock_responses_server_sequence_unchecked(responses).await;
+    let codex_home = TempDir::new()?;
+    create_config_toml(codex_home.path(), &server.uri(), "never")?;
+    let mut mcp = McpProcess::new(codex_home.path()).await?;
+
+    let message = timeout(
+        DEFAULT_READ_TIMEOUT,
+        mcp.initialize_with_client_info(ClientInfo {
+            name: "codex-backend".to_string(),
+            title: Some("Codex Backend".to_string()),
+            version: "0.1.0".to_string(),
+        }),
+    )
+    .await??;
+
+    let JSONRPCMessage::Response(response) = message else {
+        anyhow::bail!("expected initialize response, got {message:?}");
+    };
+    let InitializeResponse { user_agent, .. } = to_response::<InitializeResponse>(response)?;
+
+    assert!(user_agent.starts_with("codex_cli_rs/"));
+    Ok(())
+}
+
 #[tokio::test]
 async fn initialize_respects_originator_override_env_var() -> Result<()> {
     let responses = Vec::new();