[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/turn_context.rs

@@ -126,7 +126,6 @@ pub struct TurnContext {
     pub(crate) developer_instructions: Option<String>,
     pub(crate) user_instructions: Option<String>,
     pub(crate) collaboration_mode: CollaborationMode,
-    pub(crate) multi_agent_mode: MultiAgentMode,
     pub(crate) multi_agent_version: MultiAgentVersion,
     pub(crate) personality: Option<Personality>,
     pub(crate) approval_policy: Constrained<AskForApproval>,
@@ -276,7 +275,6 @@ impl TurnContext {
             developer_instructions: self.developer_instructions.clone(),
             user_instructions: self.user_instructions.clone(),
             collaboration_mode,
-            multi_agent_mode: self.multi_agent_mode,
             multi_agent_version: self.multi_agent_version,
             personality: self.personality,
             approval_policy: self.approval_policy.clone(),
@@ -375,11 +373,7 @@ impl TurnContext {
             personality: self.personality,
             collaboration_mode: Some(self.collaboration_mode.clone()),
             multi_agent_version: Some(self.multi_agent_version),
-            multi_agent_mode: super::multi_agents::effective_multi_agent_mode(
-                self.multi_agent_version,
-                &self.session_source,
-                self.multi_agent_mode,
-            ),
+            multi_agent_mode: super::multi_agents::effective_multi_agent_mode(self),
             realtime_active: Some(self.realtime_active),
             effort: self.reasoning_effort.clone(),
             summary: ReasoningSummaryConfig::Auto,
@@ -563,7 +557,6 @@ impl Session {
                 .as_ref()
                 .map(LoadedAgentsMd::render),
             collaboration_mode: session_configuration.collaboration_mode.clone(),
-            multi_agent_mode: session_configuration.multi_agent_mode,
             multi_agent_version,
             personality: session_configuration.personality,
             approval_policy: session_configuration.approval_policy.clone(),