[codex-analytics] add session source to client metadata (#17374)

## Summary

Adds `thread_source` field to the existing Codex turn metadata sent to
Responses API
- Sends `thread_source: "user"` for user-initiated sessions: CLI, VS
Code, and Exec
- Sends `thread_source: "subagent"` for subagent sessions
- Omits `thread_source` for MCP, custom, and unknown session sources
- Uses the existing turn metadata transport:
  - HTTP requests send through the `x-codex-turn-metadata` header
- WebSocket `response.create` requests send through
`client_metadata["x-codex-turn-metadata"]`

## Testing
- `cargo test -p codex-protocol
session_source_thread_source_name_classifies_user_and_subagent_sources`
- `cargo test -p codex-core turn_metadata_state`
- `cargo test -p codex-core --test responses_headers
responses_stream_includes_turn_metadata_header_for_git_workspace_e2e --
--nocapture`

codex-rs/core/tests/responses_headers.rs

@@ -437,6 +437,12 @@ async fn responses_stream_includes_turn_metadata_header_for_git_workspace_e2e()
             .and_then(serde_json::Value::as_str),
         Some("none")
     );
+    assert_eq!(
+        initial_parsed
+            .get("thread_source")
+            .and_then(serde_json::Value::as_str),
+        Some("user")
+    );
 
     let git_config_global = cwd.join("empty-git-config");
     std::fs::write(&git_config_global, "").expect("write empty git config");
@@ -528,6 +534,18 @@ async fn responses_stream_includes_turn_metadata_header_for_git_workspace_e2e()
         .get("turn_id")
         .and_then(serde_json::Value::as_str)
         .expect("second turn_id should be present");
+    assert_eq!(
+        first_parsed
+            .get("thread_source")
+            .and_then(serde_json::Value::as_str),
+        Some("user")
+    );
+    assert_eq!(
+        second_parsed
+            .get("thread_source")
+            .and_then(serde_json::Value::as_str),
+        Some("user")
+    );
     assert_eq!(
         first_turn_id, second_turn_id,
         "requests should share turn_id"