[codex] Steer budget-limited goal extension turns (#23718)

## What
- Add a small extension capability for injecting model-visible response
items into the active turn
- Have the goal extension inject hidden goal-context steering when
tool-finish accounting reaches `BudgetLimited`
- Cover the extension backend path with an assertion on the injected
steering item

## Why
PR #23696 persists and emits the budget-limited goal update from
tool-finish accounting, but it leaves the model unaware of that
transition. The existing core runtime steers the model to wrap up in
this case; the extension path should do the same through an explicit
host capability.

## Testing
- `just fmt`
- `cargo test -p codex-goal-extension`
- `cargo test -p codex-extension-api`

codex-rs/core/src/context/contextual_user_message_tests.rs

@@ -31,10 +31,7 @@ fn detects_subagent_notification_fragment_case_insensitively() {
 
 #[test]
 fn detects_goal_context_fragment() {
-    let text = GoalContext {
-        prompt: "Continue working toward the active thread goal.".to_string(),
-    }
-    .render();
+    let text = GoalContext::new("Continue working toward the active thread goal.").render();
 
     assert!(is_contextual_user_fragment(&ContentItem::InputText {
         text
@@ -43,9 +40,9 @@ fn detects_goal_context_fragment() {
 
 #[test]
 fn contextual_user_fragment_is_dyn_compatible() {
-    let fragment: Box<dyn ContextualUserFragment> = Box::new(GoalContext {
-        prompt: "Continue working toward the active thread goal.".to_string(),
-    });
+    let fragment: Box<dyn ContextualUserFragment> = Box::new(GoalContext::new(
+        "Continue working toward the active thread goal.",
+    ));
 
     assert_eq!(
         fragment.render(),

codex-rs/core/src/context/goal_context.rs

@@ -1,10 +1,33 @@
 //! Hidden user-context fragment for runtime-owned goal steering prompts.
 
 use super::ContextualUserFragment;
+use codex_protocol::models::ContentItem;
+use codex_protocol::models::ResponseInputItem;
 
+/// Hidden runtime-owned goal steering context injected into model input.
 #[derive(Debug, Clone, PartialEq)]
-pub(crate) struct GoalContext {
-    pub(crate) prompt: String,
+pub struct GoalContext {
+    prompt: String,
+}
+
+impl GoalContext {
+    /// Creates goal context around an already-rendered steering prompt.
+    pub fn new(prompt: impl Into<String>) -> Self {
+        Self {
+            prompt: prompt.into(),
+        }
+    }
+
+    /// Converts the registered fragment into an active-turn injectable item.
+    pub fn into_response_input_item(self) -> ResponseInputItem {
+        ResponseInputItem::Message {
+            role: <Self as ContextualUserFragment>::role().to_string(),
+            content: vec![ContentItem::InputText {
+                text: self.render(),
+            }],
+            phase: None,
+        }
+    }
 }
 
 impl ContextualUserFragment for GoalContext {

codex-rs/core/src/context/mod.rs

@@ -40,7 +40,7 @@ pub(crate) use environment_context::EnvironmentContext;
 pub use fragment::ContextualUserFragment;
 pub(crate) use fragment::FragmentRegistration;
 pub(crate) use fragment::FragmentRegistrationProxy;
-pub(crate) use goal_context::GoalContext;
+pub use goal_context::GoalContext;
 pub(crate) use guardian_followup_review_reminder::GuardianFollowupReviewReminder;
 pub(crate) use hook_additional_context::HookAdditionalContext;
 pub(crate) use image_generation_instructions::ImageGenerationInstructions;