refactor(home): 校正面 15 个状态从 Home 下沉

Home() useState 66->52, useRef 41->39. Shell-facing fields merge into one object;
subtree state lives in useRectificationSurface. Chat props 20->7. Growth contract
rebaselined. Zero behavior/copy change.

frontend/src/components/conversational-birth-time-rectification.tsx

@@ -31,7 +31,7 @@ export type PersistedRectificationTurn = Readonly<{
   }> | null;
 }>;
 
-export type ConversationalBirthTimeRectificationProps = Readonly<{
+export type RectificationChatPanel = Readonly<{
   caseId: string;
   sessionId: string;
   readonly: boolean;
@@ -39,23 +39,44 @@ export type ConversationalBirthTimeRectificationProps = Readonly<{
   initialTurns: readonly PersistedRectificationTurn[];
   /** The Case snapshot read together with the turns before the surface mounted; null when hydration failed. */
   initialSnapshot: RectificationCaseSnapshotPayload | null;
+  pendingConsultationQuestion?: string | null;
+  headerSlot: HTMLElement | null;
+  onMessagesChange?: (messages: ChatMessage[]) => void;
+  onCompleted?: () => void;
+  onPendingChange?: (pending: boolean) => void;
+  onProfileIncomplete?: () => void;
+  onOpeningConsumed?: () => void;
+  onRestart?: () => void;
+}>;
+
+export type ConversationalBirthTimeRectificationProps = Readonly<{
   /** The declared birth minute from the profile, shown on the board before any candidate exists. */
   declaredTime: string | null;
   models: readonly PublicLanguageModel[];
   selectedModelId: string;
   onSelectModel: (modelId: string) => void;
-  onMessagesChange?: (messages: ChatMessage[]) => void;
-  onCompleted?: () => void;
-  onPendingChange?: (pending: boolean) => void;
-  onProfileIncomplete?: () => void;
   onOpenBilling?: (options?: { source?: string }) => void;
   onSaved?: (time: string, status: "accepted" | "confirmed") => void;
-  onOpeningConsumed?: () => void;
-  pendingConsultationQuestion?: string | null;
-  onRestart?: () => void;
-  headerSlot: HTMLElement | null;
+  panel: RectificationChatPanel;
 }>;
 
-export function ConversationalBirthTimeRectification(props: ConversationalBirthTimeRectificationProps) {
+export function ConversationalBirthTimeRectification({
+  declaredTime,
+  models,
+  selectedModelId,
+  onSelectModel,
+  onOpenBilling,
+  onSaved,
+  panel,
+}: ConversationalBirthTimeRectificationProps) {
+  const props = {
+    declaredTime,
+    models,
+    selectedModelId,
+    onSelectModel,
+    onOpenBilling,
+    onSaved,
+    ...panel,
+  };
   return <RectificationAgenticChat {...props} />;
 }