[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/thread_manager_tests.rs

@@ -404,7 +404,6 @@ async fn start_thread_keeps_internal_threads_hidden_from_normal_lookups() {
             thread_source: None,
             dynamic_tools: Vec::new(),
             metrics_service_name: None,
-            multi_agent_mode: None,
             parent_trace: None,
             environments: Vec::new(),
             thread_extension_init: Default::default(),
@@ -545,7 +544,6 @@ async fn start_thread_seeds_extension_data_for_mcp_and_lifecycle_contributors()
             thread_source: None,
             dynamic_tools: Vec::new(),
             metrics_service_name: None,
-            multi_agent_mode: None,
             parent_trace: None,
             environments: Vec::new(),
             thread_extension_init: selected_root_init("selected-a", "env-a"),
@@ -561,7 +559,6 @@ async fn start_thread_seeds_extension_data_for_mcp_and_lifecycle_contributors()
             thread_source: None,
             dynamic_tools: Vec::new(),
             metrics_service_name: None,
-            multi_agent_mode: None,
             parent_trace: None,
             environments: Vec::new(),
             thread_extension_init: selected_root_init("selected-b", "env-b"),
@@ -654,7 +651,6 @@ async fn resume_and_fork_do_not_restore_thread_environments_from_rollout() {
             thread_source: None,
             dynamic_tools: Vec::new(),
             metrics_service_name: None,
-            multi_agent_mode: None,
             parent_trace: None,
             environments: environments.clone(),
             thread_extension_init: Default::default(),
@@ -938,7 +934,6 @@ async fn resume_stopped_thread_from_rollout_preserves_thread_source() {
             thread_source: Some(ThreadSource::User),
             dynamic_tools: Vec::new(),
             metrics_service_name: None,
-            multi_agent_mode: None,
             parent_trace: None,
             environments: Vec::new(),
             thread_extension_init: Default::default(),