Add per-turn multi-agent mode (#28685)

## Why

Multi-agent v2 currently carries an explicit-request-only delegation
rule in its static usage hint. That provides a safe default, but it
prevents clients from selecting proactive delegation per turn without
changing static guidance or rewriting prior model context.

This change makes delegation mode a session selection that can be
updated through `turn/start`, while deriving the effective model-visible
mode separately for each turn. Eligible multi-agent v2 turns remain
explicit-request-only unless proactive mode is both selected and
enabled.

## What changed

- Add the experimental `turn/start.multiAgentMode` parameter with
`explicitRequestOnly` and `proactive` values. Omission retains the
loaded session's current optional selection.
- Add the default-off `features.multi_agent_mode` feature gate. Eligible
multi-agent v2 turns use the selected mode when enabled; an unset
selection or disabled gate resolves to `explicitRequestOnly`.
- Treat mode prompting as inapplicable for multi-agent v1 and other
unsupported session configurations, producing no multi-agent mode
developer message rather than rejecting the turn.
- Move the explicit-request-only rule out of the static v2 usage hint
and into a bounded, tagged developer context fragment.
- Emit the effective mode in initial context and only when that
effective mode changes on later turns.
- Persist the effective mode in `TurnContextItem` as the durable
baseline for resume and context-update comparisons.

Historical rollout items are not rewritten. Later mode developer
messages establish the current rule incrementally.

## Not covered

- Initial selection through `thread/start` and selected-mode reporting
from thread lifecycle/settings APIs; those are isolated in the stacked
#28792.
- A TUI control or slash command for selecting the mode.
- Persisting a preferred mode to `config.toml`; selection remains
session/turn scoped.
- Changes to multi-agent concurrency limits, tool availability, or model
catalog capability declarations.
- Rewriting historical rollout prompt items. Cold resume restores the
latest persisted effective mode when available while leaving historical
developer messages intact.

## Verification

- `CARGO_INCREMENTAL=0 just test -p codex-core multi_agent_mode`
- Focused app-server coverage verifies that `turn/start.multiAgentMode`
produces proactive developer instructions for an eligible v2 turn.

## Stack

Followed by #28792, which adds `thread/start` initialization and
lifecycle/settings observability.

codex-rs/state/src/extract.rs

@@ -368,6 +368,7 @@ mod tests {
                 personality: None,
                 collaboration_mode: None,
                 multi_agent_version: None,
+                multi_agent_mode: None,
                 realtime_active: None,
                 effort: None,
                 summary: codex_protocol::config_types::ReasoningSummary::Auto,
@@ -412,6 +413,7 @@ mod tests {
                 personality: None,
                 collaboration_mode: None,
                 multi_agent_version: None,
+                multi_agent_mode: None,
                 realtime_active: None,
                 effort: None,
                 summary: codex_protocol::config_types::ReasoningSummary::Auto,
@@ -452,6 +454,7 @@ mod tests {
                 personality: None,
                 collaboration_mode: None,
                 multi_agent_version: None,
+                multi_agent_mode: None,
                 realtime_active: None,
                 effort: Some(ReasoningEffort::High),
                 summary: codex_protocol::config_types::ReasoningSummary::Auto,
@@ -489,6 +492,7 @@ mod tests {
                 personality: None,
                 collaboration_mode: None,
                 multi_agent_version: None,
+                multi_agent_mode: None,
                 realtime_active: None,
                 effort: Some(ReasoningEffort::High),
                 summary: codex_protocol::config_types::ReasoningSummary::Auto,