feat: persist task lane state across reloads and session switches

TaskLane now saves user's in-progress answers (typed text, checked
items) to sessionStorage keyed by session ID. On reload or session
switch, the full task lane state restores — including partial work.

- TaskLane: saves tasks array to sessionStorage on every change,
  restores from sessionStorage on mount
- AssistantChatPage: saves task lane metadata (visibility, questions,
  actions, chatId) to sessionStorage, restores on mount
- Closing the task lane clears its sessionStorage entry

Co-Authored-By: Claude Opus 4.6 (1M context) <noreply@anthropic.com>

frontend/src/pages/AssistantChatPage.tsx

@@ -12,7 +12,7 @@ import { analytics } from '@/lib/analytics'
 import { toast } from '@/lib/toast'
 import { ChatSidebar, ChatSidebarCollapsedBar } from '@/components/assistant/ChatSidebar'
 import { ChatMessage } from '@/components/assistant/ChatMessage'
-import { TaskLane } from '@/components/assistant/TaskLane'
+import { TaskLane, clearTaskState } from '@/components/assistant/TaskLane'
 import { ConcludeSessionModal } from '@/components/assistant/ConcludeSessionModal'
 import type { ChatListItem, ConclusionOutcome } from '@/types/assistant-chat'
 import type { SuggestedFlow } from '@/types/copilot'
@@ -42,9 +42,27 @@ export default function AssistantChatPage() {
   const [logContent, setLogContent] = useState('')
   const [pendingUploads, setPendingUploads] = useState<PendingUpload[]>([])
   const [isDragOver, setIsDragOver] = useState(false)
-  const [activeQuestions, setActiveQuestions] = useState<QuestionItem[]>([])
-  const [activeActions, setActiveActions] = useState<ActionItem[]>([])
-  const [showTaskLane, setShowTaskLane] = useState(false)
+  const [activeQuestions, setActiveQuestions] = useState<QuestionItem[]>(() => {
+    try {
+      const saved = sessionStorage.getItem('rf-tasklane-meta')
+      if (saved) { const d = JSON.parse(saved); return d.questions || [] }
+    } catch { /* ignore */ }
+    return []
+  })
+  const [activeActions, setActiveActions] = useState<ActionItem[]>(() => {
+    try {
+      const saved = sessionStorage.getItem('rf-tasklane-meta')
+      if (saved) { const d = JSON.parse(saved); return d.actions || [] }
+    } catch { /* ignore */ }
+    return []
+  })
+  const [showTaskLane, setShowTaskLane] = useState(() => {
+    try {
+      const saved = sessionStorage.getItem('rf-tasklane-meta')
+      if (saved) { const d = JSON.parse(saved); return d.show === true && d.chatId === (urlSessionId || null) }
+    } catch { /* ignore */ }
+    return false
+  })
   const [sidebarCollapsed, setSidebarCollapsed] = useState(() =>
     localStorage.getItem('rf-chat-sidebar-collapsed') === 'true'
   )
@@ -137,6 +155,18 @@ export default function AssistantChatPage() {
   // eslint-disable-next-line react-hooks/exhaustive-deps
   }, [])
 
+  // Persist task lane metadata to sessionStorage
+  useEffect(() => {
+    try {
+      sessionStorage.setItem('rf-tasklane-meta', JSON.stringify({
+        show: showTaskLane,
+        chatId: activeChatId,
+        questions: activeQuestions,
+        actions: activeActions,
+      }))
+    } catch { /* ignore */ }
+  }, [showTaskLane, activeChatId, activeQuestions, activeActions])
+
   // Auto-scroll
   useEffect(() => {
     messagesEndRef.current?.scrollIntoView({ behavior: 'smooth' })
@@ -737,8 +767,12 @@ export default function AssistantChatPage() {
         <TaskLane
           questions={activeQuestions}
           actions={activeActions}
+          sessionId={activeChatId}
           onSubmit={handleTaskSubmit}
-          onClose={() => setShowTaskLane(false)}
+          onClose={() => {
+            setShowTaskLane(false)
+            if (activeChatId) clearTaskState(activeChatId)
+          }}
           loading={loading}
         />
       )}