Use runtime authentication for Analytics requests (#60101)

## What changed

- Honor `RuntimeAgentInstances` and the configured runtime auth mode for Analytics plan discovery and report requests to OpenAI endpoints.
- Share installation ID resolution and Codex runtime registration setup through `codex-runtime-agent-instance`.
- Preserve typed runtime authentication errors so expired credentials retain the “Sign in again to load Analytics” guidance.

## Testing

Add coverage for both runtime auth modes across regional and staging endpoints, fresh assertions for each request, sign-in guidance after bootstrap failure, redirect rejection, and invalid organization/project selectors.

GitOrigin-RevId: 50e0d959b3abd81ebe7a6a584e272f14cf52e504

codex-rs/runtime-agent-instance/src/manager.rs

@@ -80,6 +80,24 @@ impl RuntimeAuthManager {
         }
     }
 
+    /// Construct a Codex runtime owner without registering it or generating its key.
+    pub fn for_codex(
+        credentials: Arc<AuthManager>,
+        chatgpt_base_url: &str,
+        installation_id: &str,
+    ) -> Self {
+        Self::for_chatgpt(
+            credentials,
+            installation_id.to_owned(),
+            chatgpt_base_url.to_owned(),
+            RuntimeRegistrationMetadata {
+                harness: Some("codex".to_string()),
+                harness_version: Some(env!("CARGO_PKG_VERSION").to_string()),
+                role: crate::RuntimeRole::Orchestrator,
+            },
+        )
+    }
+
     pub fn registration_url(&self) -> Result<Url, RegistrationError> {
         self.login.registration_url()
     }