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/context_manager/updates.rs

@@ -106,7 +106,7 @@ fn build_multi_agent_mode_update_item(
         &next.config.multi_agent_v2,
         &next.session_source,
         next.multi_agent_mode,
-        next.features.enabled(Feature::MultiAgentMode),
+        next.config.features.enabled(Feature::MultiAgentMode),
     );
     let previous = previous?;
     if previous.multi_agent_mode == effective_multi_agent_mode {