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/core/src/client.rs

@@ -1734,19 +1734,9 @@ fn subagent_header_value(session_source: &SessionSource) -> Option<String> {
 }
 
 fn parent_thread_id_header_value(session_source: &SessionSource) -> Option<String> {
-    match session_source {
-        SessionSource::SubAgent(SubAgentSource::ThreadSpawn {
-            parent_thread_id, ..
-        }) => Some(parent_thread_id.to_string()),
-        SessionSource::Cli
-        | SessionSource::VSCode
-        | SessionSource::Exec
-        | SessionSource::Mcp
-        | SessionSource::Custom(_)
-        | SessionSource::Internal(_)
-        | SessionSource::SubAgent(_)
-        | SessionSource::Unknown => None,
-    }
+    session_source
+        .parent_thread_id()
+        .map(|parent_thread_id| parent_thread_id.to_string())
 }
 
 const RESPONSE_STREAM_CHANNEL_CAPACITY: usize = 1600;