fix(web): split rectification process talk from the spoken reply

Keep provider thinking off, classify CoT as 思考, and stop remounted sessions from firing a second opening.

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

frontend/src/app/globals.css

@@ -873,6 +873,11 @@ button:disabled { cursor: default; opacity: .45; }
 .consultation-report-analysis .message-markdown {
   color: var(--color-ink-strong);
 }
+.consultation-thinking-report .message-thinking {
+  margin-bottom: 0;
+  padding-bottom: var(--space-3);
+  border-bottom: 1px solid color-mix(in srgb, var(--color-border) 72%, transparent);
+}
 .message-markdown ul.markdown-list,
 .message-markdown ol.markdown-list {
   display: grid;

frontend/src/app/page.tsx

@@ -4034,7 +4034,7 @@ export default function Home() {
 
         {rectificationSurfaceOpen && rectificationCaseId && (
           <ConversationalBirthTimeRectification
-            key={`${rectificationSessionId}-${rectificationCaseId}-${rectificationTurns.at(-1)?.id ?? "loading"}`}
+            key={`${rectificationSessionId}-${rectificationCaseId}-${rectificationTurns.length > 0 ? "ready" : "loading"}`}
             caseId={rectificationCaseId}
             sessionId={rectificationSessionId ?? ""}
             readonly={rectificationReadonly}
@@ -4044,7 +4044,13 @@ export default function Home() {
             selectedModelId={activeSession?.modelId ?? ""}
             onSelectModel={(modelId) => void selectSessionModel(modelId)}
             onMessagesChange={handleRectificationMessagesChange}
-            onCompleted={() => void refreshAccount()}
+            onOpeningConsumed={() => setRectificationShouldStartOpening(false)}
+            onCompleted={() => {
+              void refreshAccount();
+              if (rectificationCaseId && rectificationSessionId) {
+                void refreshRectificationCase(rectificationCaseId, rectificationSessionId);
+              }
+            }}
             onPendingChange={setRectificationMutationPending}
             onProfileIncomplete={handleRectificationProfileIncomplete}
             onSaved={() => void refreshAccount()}