[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/codex_thread.rs

@@ -8,7 +8,6 @@ use codex_otel::SessionTelemetry;
 use codex_protocol::ThreadId;
 use codex_protocol::config_types::ApprovalsReviewer;
 use codex_protocol::config_types::CollaborationMode;
-use codex_protocol::config_types::MultiAgentMode;
 use codex_protocol::config_types::Personality;
 use codex_protocol::config_types::ReasoningSummary;
 use codex_protocol::config_types::WindowsSandboxLevel;
@@ -72,7 +71,6 @@ pub struct ThreadConfigSnapshot {
     pub reasoning_summary: Option<ReasoningSummary>,
     pub personality: Option<Personality>,
     pub collaboration_mode: CollaborationMode,
-    pub multi_agent_mode: MultiAgentMode,
     pub session_source: SessionSource,
     pub forked_from_thread_id: Option<ThreadId>,
     pub parent_thread_id: Option<ThreadId>,
@@ -154,7 +152,6 @@ pub struct CodexThreadSettingsOverrides {
     pub summary: Option<ReasoningSummary>,
     pub service_tier: Option<Option<String>>,
     pub collaboration_mode: Option<CollaborationMode>,
-    pub multi_agent_mode: Option<MultiAgentMode>,
     pub personality: Option<Personality>,
 }
 
@@ -375,7 +372,6 @@ impl CodexThread {
             summary,
             service_tier,
             collaboration_mode,
-            multi_agent_mode,
             personality,
         } = overrides;
         let collaboration_mode = if let Some(collaboration_mode) = collaboration_mode {
@@ -399,7 +395,6 @@ impl CodexThread {
             active_permission_profile,
             windows_sandbox_level,
             collaboration_mode: Some(collaboration_mode),
-            multi_agent_mode,
             reasoning_summary: summary,
             service_tier,
             personality,