store and expose parent_thread_id on Threads (#25113)

## Why

This PR
https://github.com/openai/codex/pull/24161#discussion_r3325692763
revealed a subagent data modeling issue, where we overloaded
`forked_from_id` to also mean `parent_thread_id`. That's incorrect since
guardian and review subagents can be a subagent and NOT fork the main
thread's history.

The solution here is to explicitly store a new `parent_thread_id` on
`SessionMeta`, alongside `forked_from_id` which already exists. While
we're at it, also expose it in the app-server protocol on the `Thread`
object.

A thread->subagent relationship and a fork of thread history are
orthogonal concepts.

## What Changed

- Added top-level `parent_thread_id` persistence on `SessionMeta` and
runtime/session plumbing through `SessionConfiguredEvent`,
`CodexSpawnArgs`, `SessionConfiguration`, `ThreadConfigSnapshot`,
`TurnContext`, and `ModelClient`.
- Made turn metadata, request headers, analytics, and subagent-start
events read the separate runtime/top-level parent field instead of
deriving general parent lineage from `SessionSource` or
`forked_from_thread_id`.
- Passed parent lineage separately at delegated subagent, review,
guardian, agent-job, and multi-agent spawn construction sites;
copied-history fork lineage remains derived only from `InitialHistory`.
- Persisted and exposed parent lineage through rollout/thread-store
projections and app-server v2 `Thread.parentThreadId`.
- Updated app-server README text and regenerated app-server schema
fixtures for the additive `parentThreadId` response field.

codex-rs/app-server-protocol/src/protocol/common.rs

@@ -2328,6 +2328,7 @@ mod tests {
                     id: "67e55044-10b1-426f-9247-bb680e5fe0c8".to_string(),
                     session_id: "67e55044-10b1-426f-9247-bb680e5fe0c7".to_string(),
                     forked_from_id: None,
+                    parent_thread_id: None,
                     preview: "first prompt".to_string(),
                     ephemeral: true,
                     model_provider: "openai".to_string(),
@@ -2370,6 +2371,7 @@ mod tests {
                         "id": "67e55044-10b1-426f-9247-bb680e5fe0c8",
                         "sessionId": "67e55044-10b1-426f-9247-bb680e5fe0c7",
                         "forkedFromId": null,
+                        "parentThreadId": null,
                         "preview": "first prompt",
                         "ephemeral": true,
                         "modelProvider": "openai",

codex-rs/app-server-protocol/src/protocol/v2/tests.rs

@@ -142,6 +142,7 @@ fn thread_resume_response_round_trips_initial_turns_page() {
             id: "thr_123".to_string(),
             session_id: "thr_123".to_string(),
             forked_from_id: None,
+            parent_thread_id: None,
             preview: String::new(),
             ephemeral: false,
             model_provider: "openai".to_string(),
@@ -3581,6 +3582,7 @@ fn thread_lifecycle_responses_default_missing_optional_fields() {
     let fork: ThreadForkResponse = serde_json::from_value(response).expect("thread/fork response");
 
     assert_eq!(start.instruction_sources, Vec::<AbsolutePathBuf>::new());
+    assert_eq!(start.thread.parent_thread_id, None);
     assert_eq!(resume.instruction_sources, Vec::<AbsolutePathBuf>::new());
     assert_eq!(fork.instruction_sources, Vec::<AbsolutePathBuf>::new());
     assert_eq!(start.active_permission_profile, None);

codex-rs/app-server-protocol/src/protocol/v2/thread_data.rs

@@ -108,6 +108,8 @@ pub struct Thread {
     pub session_id: String,
     /// Source thread id when this thread was created by forking another thread.
     pub forked_from_id: Option<String>,
+    /// The ID of the parent thread. This will only be set if this thread is a subagent.
+    pub parent_thread_id: Option<String>,
     /// Usually the first user message in the thread, if available.
     pub preview: String,
     /// Whether the thread is ephemeral and should not be materialized on disk.