[codex] Add Ultra reasoning effort (#29899)

## Why

Ultra should be one user-facing reasoning selection for work that
benefits from both maximum reasoning and proactive multi-agent
delegation. Without it, clients must coordinate maximum reasoning with
the experimental `multiAgentMode` setting, even though the inference
backend still expects its existing `max` effort value.

This change makes reasoning effort the source of truth: clients select
`ultra`, core derives proactive multi-agent behavior when the turn is
eligible for multi-agent V2, and inference requests continue to use the
backend-compatible `max` value.

## What changed

- Add `ultra` as a first-class reasoning effort and preserve
model-catalog ordering when exposing it to clients.
- Convert `ultra` to `max` at the inference request boundary, including
Responses HTTP/WebSocket requests, startup prewarm, compaction, and
memory summarization.
- Derive effective multi-agent mode per turn from effective reasoning
effort:
  - eligible multi-agent V2 + `ultra` → `proactive`
  - eligible multi-agent V2 + any other effort → `explicitRequestOnly`
- V1 or otherwise ineligible sessions → no multi-agent mode instruction
- Keep the derived effective mode in turn context history so successive
turns can emit a developer-message update only when the effective mode
changes.
- Remove selected multi-agent mode from core session configuration, turn
construction, thread settings, resume/fork restoration, and subagent
spawn plumbing. Subagents inherit reasoning effort and derive their own
effective mode.
- Retain the experimental app-server `multiAgentMode` fields for wire
compatibility while marking them deprecated. Request values are accepted
but ignored; compatibility response fields report `explicitRequestOnly`.
- Display Ultra in the TUI using the order supplied by `model/list`.

## Validation

- `just test -p codex-core ultra_reasoning_uses_max_for_requests`
- `just test -p codex-tui model_reasoning_selection_popup`

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

@@ -52,7 +52,6 @@ pub(crate) struct SessionConfiguration {
     pub(super) provider: ModelProviderInfo,
 
     pub(super) collaboration_mode: CollaborationMode,
-    pub(super) multi_agent_mode: MultiAgentMode,
     pub(super) model_reasoning_summary: Option<ReasoningSummaryConfig>,
     pub(super) service_tier: Option<String>,
 
@@ -195,7 +194,6 @@ impl SessionConfiguration {
             reasoning_summary: self.model_reasoning_summary,
             personality: self.personality,
             collaboration_mode: self.collaboration_mode.clone(),
-            multi_agent_mode: self.multi_agent_mode,
             session_source: self.session_source.clone(),
             forked_from_thread_id: self.forked_from_thread_id,
             parent_thread_id: self.parent_thread_id,
@@ -233,9 +231,6 @@ impl SessionConfiguration {
         if let Some(collaboration_mode) = updates.collaboration_mode.clone() {
             next_configuration.collaboration_mode = collaboration_mode;
         }
-        if let Some(multi_agent_mode) = updates.multi_agent_mode {
-            next_configuration.multi_agent_mode = multi_agent_mode;
-        }
         if let Some(summary) = updates.reasoning_summary {
             next_configuration.model_reasoning_summary = Some(summary);
         }
@@ -430,7 +425,6 @@ pub(crate) struct SessionSettingsUpdate {
     pub(crate) active_permission_profile: Option<ActivePermissionProfile>,
     pub(crate) windows_sandbox_level: Option<WindowsSandboxLevel>,
     pub(crate) collaboration_mode: Option<CollaborationMode>,
-    pub(crate) multi_agent_mode: Option<MultiAgentMode>,
     pub(crate) reasoning_summary: Option<ReasoningSummaryConfig>,
     pub(crate) service_tier: Option<Option<String>>,
     pub(crate) final_output_json_schema: Option<Option<Value>>,