Always send reasoning parameters in Responses requests (#32206)

## What changed

- Build a reasoning payload for every Responses request and always include `reasoning.encrypted_content`.
- Remove `supports_reasoning_summaries` from model metadata and retire the `model_supports_reasoning_summaries` configuration override.
- Use configured or model-default reasoning effort without a capability gate, including for guardian reviews and tracing.

GitOrigin-RevId: 2c9f194a5d2d4d688a2235299e6358f82ab8e1ea

codex-rs/models-manager/src/model_info.rs

@@ -21,11 +21,6 @@ const LOCAL_PRAGMATIC_TEMPLATE: &str = "You are a deeply pragmatic, effective so
 const PERSONALITY_PLACEHOLDER: &str = "{{ personality }}";
 
 pub fn with_config_overrides(mut model: ModelInfo, config: &ModelsManagerConfig) -> ModelInfo {
-    if let Some(supports_reasoning_summaries) = config.model_supports_reasoning_summaries
-        && supports_reasoning_summaries
-    {
-        model.supports_reasoning_summaries = true;
-    }
     if let Some(context_window) = config.model_context_window {
         model.context_window = Some(
             model
@@ -93,7 +88,6 @@ pub fn model_info_from_slug(slug: &str) -> ModelInfo {
         base_instructions: BASE_INSTRUCTIONS.to_string(),
         model_messages: local_personality_messages_for_slug(slug),
         include_skills_usage_instructions: false,
-        supports_reasoning_summaries: false,
         default_reasoning_summary: ReasoningSummary::Auto,
         support_verbosity: false,
         default_verbosity: None,