fix(workbench): complete profile and channel flows

apps/web_v1/src/pages/projects/project-ai.tsx

@@ -50,7 +50,7 @@ export function ProjectAi({
     setSelectedExpertID(null)
     setExpertQuery('')
     setExpertCategory('all')
-    setPrompt('')
+    setPrompt(readPromptDraft(projectId))
     setLoading(true)
     setLoadingExperts(true)
     setCreating(false)
@@ -91,6 +91,15 @@ export function ProjectAi({
     }
   }, [onListExperts, onListSessions, projectId])
 
+  useEffect(() => {
+    try {
+      if (prompt) localStorage.setItem(promptDraftKey(projectId), prompt)
+      else localStorage.removeItem(promptDraftKey(projectId))
+    } catch {
+      // Draft persistence is best effort; an unavailable browser store must not block chat.
+    }
+  }, [projectId, prompt])
+
   const selectedSession = useMemo(
     () => sessions.find((session) => session.id === selectedSessionID) ?? null,
     [selectedSessionID, sessions],
@@ -345,3 +354,15 @@ function sessionTitle(message: string) {
   const characters = Array.from(firstLine)
   return characters.length > 36 ? `${characters.slice(0, 36).join('')}…` : firstLine
 }
+
+function promptDraftKey(projectId: string) {
+  return `senlin:ai:prompt:${projectId}`
+}
+
+function readPromptDraft(projectId: string) {
+  try {
+    return localStorage.getItem(promptDraftKey(projectId)) ?? ''
+  } catch {
+    return ''
+  }
+}