Expose thread-level multi-agent mode (#28792)

## Why

Once multi-agent mode can be selected per turn, clients also need to
choose the initial selection when creating a thread and observe that
selection through lifecycle and settings APIs.

The selected value is intentionally distinct from the effective
model-visible value: no client selection is represented as `null`, even
though an eligible multi-agent v2 turn derives `explicitRequestOnly` as
its effective default.

## What changed

- Add the optional experimental `thread/start.multiAgentMode` parameter
and pass it through thread creation.
- Preserve an omitted initial value as an unset selection rather than
eagerly storing `explicitRequestOnly`.
- Apply an explicit `thread/start` selection to the first turn through
the session configuration established at thread creation.
- Restore the latest persisted effective mode as the selected baseline
on cold resume when rollout history contains one.
- Inherit the optional selected mode from a loaded parent when creating
related runtime threads.
- Return the current selected `multiAgentMode` from `thread/start`,
`thread/resume`, `thread/fork`, and thread settings, using `null` when
no mode is selected.
- Keep lifecycle reporting independent from model capability and feature
eligibility; core turn construction remains responsible for calculating
and persisting the effective mode.

## Not covered

- Clearing an existing loaded-session selection back to unset through
`turn/start`; omitted or `null` currently retains the session's
selection.
- A TUI control, slash command, or `config.toml` preference.

## Verification

- `CARGO_INCREMENTAL=0 just test -p codex-app-server-protocol`
- `CARGO_INCREMENTAL=0 just test -p codex-app-server multi_agent_mode`

The focused app-server coverage verifies explicit `thread/start`
initialization, first-turn prompting, nullable reporting for an omitted
selection, and retention of selections that are not currently
runtime-eligible.

## Stack

Stacked on #28685. This PR contains only the thread initialization and
lifecycle/settings API layer.

codex-rs/core/src/session/handlers.rs

@@ -178,6 +178,7 @@ async fn thread_settings_applied_event(sess: &Session) -> EventMsg {
             reasoning_summary: snapshot.reasoning_summary,
             personality: snapshot.personality,
             collaboration_mode: snapshot.collaboration_mode,
+            multi_agent_mode: snapshot.multi_agent_mode,
         },
     })
 }

codex-rs/core/src/session/mod.rs

@@ -445,6 +445,7 @@ pub(crate) struct CodexSpawnArgs {
     pub(crate) attestation_provider: Option<Arc<dyn AttestationProvider>>,
     pub(crate) external_time_provider: Option<Arc<dyn TimeProvider>>,
     pub(crate) inherited_multi_agent_version: Option<MultiAgentVersion>,
+    pub(crate) initial_multi_agent_mode: Option<MultiAgentMode>,
 }
 
 pub(crate) fn resolve_multi_agent_version(
@@ -529,6 +530,7 @@ impl Codex {
             attestation_provider,
             external_time_provider,
             inherited_multi_agent_version,
+            initial_multi_agent_mode,
         } = args;
         let (tx_sub, rx_sub) = async_channel::bounded(SUBMISSION_CHANNEL_CAPACITY);
         let (tx_event, rx_event) = async_channel::unbounded();
@@ -583,7 +585,7 @@ impl Codex {
             .await;
         let multi_agent_version =
             resolve_multi_agent_version(&conversation_history, inherited_multi_agent_version);
-        let multi_agent_mode = conversation_history.get_multi_agent_mode();
+        let multi_agent_mode = initial_multi_agent_mode;
         config
             .validate_multi_agent_v2_config()
             .map_err(|err| CodexErr::InvalidRequest(err.to_string()))?;
@@ -3249,7 +3251,10 @@ impl Session {
             &turn_context.config.multi_agent_v2,
             &session_source,
             turn_context.multi_agent_mode,
-            turn_context.features.enabled(Feature::MultiAgentMode),
+            turn_context
+                .config
+                .features
+                .enabled(Feature::MultiAgentMode),
         ) {
             items.push(ContextualUserFragment::into(
                 MultiAgentModeInstructions::new(multi_agent_mode),

codex-rs/core/src/session/tests/guardian_tests.rs

@@ -738,6 +738,7 @@ async fn guardian_subagent_does_not_inherit_parent_exec_policy_rules() {
         attestation_provider: None,
         external_time_provider: None,
         inherited_multi_agent_version: None,
+        initial_multi_agent_mode: None,
     })
     .await
     .expect("spawn guardian subagent");

codex-rs/core/src/session/turn_context.rs

@@ -388,7 +388,7 @@ impl TurnContext {
                 &self.config.multi_agent_v2,
                 &self.session_source,
                 self.multi_agent_mode,
-                self.features.enabled(Feature::MultiAgentMode),
+                self.config.features.enabled(Feature::MultiAgentMode),
             ),
             realtime_active: Some(self.realtime_active),
             effort: self.reasoning_effort.clone(),