fix(rectification): pin the adopt card and drop casual adopt copy

The time card stayed under an earlier collect question, and the close said to just use a time for now. Keep the card on the delivery turn and present the analysis as this round's result.

Co-authored-by: Cursor <cursoragent@cursor.com>

frontend/src/components/rectification-agentic-chat.tsx

@@ -95,7 +95,15 @@ import {
 import { ModelSelector } from "./model-selector";
 import { RectificationBoard, RectificationBoardPeek } from "./rectification-board";
 import { RectificationChoiceCard } from "./rectification-choice-card";
-import { copyTextForMessage, parseTurnQuestion, questionIsAnswered, type TurnQuestion } from "@/lib/rectification-agentic/v9/turn-question";
+import {
+  applyLiveCandidateOffer,
+  copyTextForMessage,
+  interviewQuestionBlocksAdoptOffer,
+  parseTurnQuestion,
+  persistedOfferFromTurn,
+  questionIsAnswered,
+  type TurnQuestion,
+} from "@/lib/rectification-agentic/v9/turn-question";
 import { Button } from "@/components/ui/button";
 
 type PersistedTurn = Readonly<{
@@ -264,9 +272,11 @@ function mergeTurnQuestions(current: RenderMessage[], turns: readonly unknown[])
     return {
       ...message,
       question: question ?? undefined,
-      candidateOffer: next?.offerResultId
-        ? { resultId: next.offerResultId }
-        : message.candidateOffer,
+      candidateOffer: persistedOfferFromTurn(
+        next?.offerResultId,
+        message.candidateOffer,
+        true,
+      ),
     };
   });
 }
@@ -609,25 +619,11 @@ export function RectificationAgenticChat(props: RectificationAgenticChatProps) {
     if (!canOffer && !adopted) return;
     const resultId = candidateResult.resultId;
     queueMicrotask(() => {
-      setMessages((current) => {
-        if (current.some((message) => message.candidateOffer?.resultId === resultId)) return current;
-        if (adopted && current.some((message) => message.candidateOffer)) {
-          return current.map((message) => (
-            message.candidateOffer ? { ...message, candidateOffer: { resultId } } : message
-          ));
-        }
-        if (!canOffer || adopted) return current;
-        const owner = [...current].reverse().find((message) => (
-          message.role === "assistant"
-          && message.state === "settled"
-          && Boolean(message.text)
-          && !message.failed
-        ));
-        if (!owner) return current;
-        return current.map((message) => (
-          message.renderKey === owner.renderKey ? { ...message, candidateOffer: { resultId } } : message
-        ));
-      });
+      setMessages((current) => applyLiveCandidateOffer(current, {
+        resultId,
+        canOffer,
+        adopted,
+      }));
     });
   }, [candidateResult]);
 
@@ -1375,13 +1371,16 @@ export function RectificationAgenticChat(props: RectificationAgenticChatProps) {
     && regeneratingMessageKey === null,
   );
   const canOfferCards = canShowRectificationSelectionCards(candidateResult);
-  const persistedOfferKey = messages.find((message) => message.candidateOffer)?.renderKey;
+  const persistedOfferKey = [...messages].reverse().find((message) => message.candidateOffer)?.renderKey;
   const selectionCardMessageKey = persistedOfferKey
     ?? (canOfferCards && !candidateResult?.selectedTime ? latestSettledAssistant?.renderKey : undefined);
   const showSelectionCards = Boolean(
     candidateResult
     && selectionCardMessageKey
-    && (canOfferCards || Boolean(candidateResult.selectedTime)),
+    && (canOfferCards || Boolean(candidateResult.selectedTime))
+    && !messages.some((message) => (
+      interviewQuestionBlocksAdoptOffer(message.question, Boolean(candidateResult.selectedTime))
+    )),
   );
   const showReadonlyRange = Boolean(
     canShowRectificationReadonlyRange(candidateResult)