[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/analytics/src/reducer.rs

@@ -26,7 +26,6 @@ use crate::events::plugin_state_event_type;
 use crate::events::subagent_parent_thread_id;
 use crate::events::subagent_source_name;
 use crate::events::subagent_thread_started_event_request;
-use crate::events::thread_source_name;
 use crate::facts::AnalyticsFact;
 use crate::facts::AnalyticsJsonRpcError;
 use crate::facts::AppMentionedInput;
@@ -107,7 +106,7 @@ impl ThreadMetadataState {
             | SessionSource::Unknown => (None, None),
         };
         Self {
-            thread_source: thread_source_name(session_source),
+            thread_source: session_source.thread_source_name(),
             initialization_mode,
             subagent_source,
             parent_thread_id,