Improve goal continuation based on feedback (#22045)

## Summary

This PR updates the goal continuation prompt to address feedback from
early adopters. There are two primary changes:

1. Goal continuation and budget-limit steering prompts now use hidden
user-context messages instead of hidden developer messages.
2. The goal continuation prompt is refined to improve the model's
ability to fully complete the active goal rather than stop at a smaller
or merely passing subset.

The user-message transition is important for two reasons. First, it
eliminates an issue where older steering messages could be responded to
again after a new turn. Second, it works better with compaction because
user messages are treated differently from developer messages during
compaction.

The prompt refinements make persistence explicit, ground work in current
evidence, encourage `update_plan` for multi-step progress visibility,
and require stronger completion audits before calling `update_goal`. It
also removes the elapsed-time reporting in the prompt; I saw evidence
that this was causing the model to shortcut work as it became nervous
about time.

These changes were tested with evals. Chriss4123 has also been running
independent evals in
[#19910](https://github.com/openai/codex/issues/19910), and many of the
improvements in this PR were suggested by him.

## Verification

- Tested with evals.
- Added and updated focused `codex-core` coverage for hidden goal user
context, continuation and budget-limit request shape, prompt rendering,
and objective delimiter escaping.

codex-rs/core/src/session/tests.rs

@@ -7707,7 +7707,7 @@ async fn active_goal_continuation_runs_again_after_no_tool_turn() -> anyhow::Res
             .expect("goal mode should be enableable in tests");
     });
     let test = builder.build(&server).await?;
-    let _responses = mount_sse_sequence(
+    let responses = mount_sse_sequence(
         &server,
         vec![
             sse(vec![
@@ -7770,6 +7770,25 @@ async fn active_goal_continuation_runs_again_after_no_tool_turn() -> anyhow::Res
     })
     .await??;
 
+    let continuation_request = responses
+        .requests()
+        .into_iter()
+        .find(|request| request.body_contains_text("<goal_context>"))
+        .expect("expected a goal continuation request");
+    let body = continuation_request.body_json();
+    let goal_context_message = body["input"]
+        .as_array()
+        .expect("input should be an array")
+        .iter()
+        .find(|item| item.to_string().contains("<goal_context>"))
+        .expect("goal context message should be present");
+    assert_eq!(goal_context_message["role"].as_str(), Some("user"));
+    assert!(
+        goal_context_message
+            .to_string()
+            .contains("Continue working toward the active thread goal.")
+    );
+
     Ok(())
 }
 
@@ -7970,10 +7989,12 @@ async fn budget_limited_accounting_steers_active_turn_without_aborting() -> anyh
     let [ResponseInputItem::Message { role, content, .. }] = pending_input.as_slice() else {
         panic!("expected one budget-limit steering message, got {pending_input:#?}");
     };
-    assert_eq!("developer", role);
+    assert_eq!("user", role);
     let [ContentItem::InputText { text }] = content.as_slice() else {
         panic!("expected one text span in budget-limit steering message, got {content:#?}");
     };
+    assert!(text.starts_with("<goal_context>"));
+    assert!(text.trim_end().ends_with("</goal_context>"));
     assert!(text.contains("budget_limited"));
     assert!(text.to_lowercase().contains("wrap up this turn soon"));
     assert!(sess.active_turn.lock().await.is_some());