Add subagent lineage metadata for responsesapi (#24161)

## Why

We recently added `forked_from_thread_id` which lets us trace where a
thread's _context_ comes from, but we also want to understand subagent
lineage (e.g. which parent thread spawned this subagent? what kind of
subagent is it?) which is orthogonal.

This PR adds `parent_thread_id` and `subagent_kind` to the
`x-codex-turn-metadata` header sent to ResponsesAPI.

## What changed

- Adds `parent_thread_id` and `subagent_kind` to core-owned
`x-codex-turn-metadata`.
- Restores persisted `SessionSource` and `ThreadSource` from resumed
session metadata so cold-resumed subagent threads keep their lineage on
later Responses API requests.
- Centralizes parent-thread extraction on `SessionSource` /
`SubAgentSource` and reuses it in the Responses client, analytics, agent
control, and state parsing paths.
- Extends reserved-key, git-enrichment, thread-spawn, and app-server v2
metadata coverage for the new lineage fields.

## Verification

- Not run locally per request.
- Added focused coverage in `core/src/turn_metadata_tests.rs` and
`app-server/tests/suite/v2/client_metadata.rs`.

codex-rs/state/src/runtime/threads.rs

@@ -960,13 +960,7 @@ pub(super) fn extract_memory_mode(items: &[RolloutItem]) -> Option<String> {
 fn thread_spawn_parent_thread_id_from_source_str(source: &str) -> Option<ThreadId> {
     let parsed_source = serde_json::from_str(source)
         .or_else(|_| serde_json::from_value::<SessionSource>(Value::String(source.to_string())));
-    match parsed_source.ok() {
-        Some(SessionSource::SubAgent(codex_protocol::protocol::SubAgentSource::ThreadSpawn {
-            parent_thread_id,
-            ..
-        })) => Some(parent_thread_id),
-        _ => None,
-    }
+    parsed_source.ok()?.parent_thread_id()
 }
 
 #[derive(Clone, Copy)]