[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/events.rs

@@ -15,7 +15,6 @@ use codex_plugin::PluginTelemetryMetadata;
 use codex_protocol::approvals::NetworkApprovalProtocol;
 use codex_protocol::models::PermissionProfile;
 use codex_protocol::models::SandboxPermissions;
-use codex_protocol::protocol::SessionSource;
 use codex_protocol::protocol::SubAgentSource;
 use serde::Serialize;
 
@@ -530,14 +529,6 @@ pub(crate) fn codex_plugin_used_metadata(
     }
 }
 
-pub(crate) fn thread_source_name(thread_source: &SessionSource) -> Option<&'static str> {
-    match thread_source {
-        SessionSource::Cli | SessionSource::VSCode | SessionSource::Exec => Some("user"),
-        SessionSource::SubAgent(_) => Some("subagent"),
-        SessionSource::Mcp | SessionSource::Custom(_) | SessionSource::Unknown => None,
-    }
-}
-
 pub(crate) fn current_runtime_metadata() -> CodexRuntimeMetadata {
     let os_info = os_info::get();
     CodexRuntimeMetadata {