feat(backend): persist tasks and generated message history

- add EntityTask domain and CRUD API backed by PostgreSQL

- relate generated messages directly to tasks and delete on task removal

- move preview generation to backend Llama endpoint

- migrate frontend task APIs from localStorage to backend endpoints

- update tests and CLAUDE rules for backend-owned LLM/persistence

frontend/src/__tests__/pages/EditTaskPage.test.tsx

@@ -61,9 +61,18 @@ const mockTask = {
   createdAt: '2026-03-26T10:00:00Z',
 }
 
+let persistedHistory: Array<{
+  id: string
+  taskId: string
+  label: string
+  content: string
+  createdAt: string
+}> = []
+
 describe('EditTaskPage', () => {
   beforeEach(() => {
     vi.clearAllMocks()
+    persistedHistory = []
     vi.mocked(entitiesApi.getEntity).mockResolvedValue(mockEntity)
     vi.mocked(tasksApi.getTask).mockResolvedValue(mockTask)
     vi.mocked(tasksApi.buildTaskPreviewPrompt).mockImplementation(
@@ -73,6 +82,10 @@ describe('EditTaskPage', () => {
     vi.mocked(tasksApi.activateTask).mockResolvedValue({ ...mockTask, active: true })
     vi.mocked(tasksApi.inactivateTask).mockResolvedValue({ ...mockTask, active: false })
     vi.mocked(tasksApi.deleteTask).mockResolvedValue(undefined)
+    vi.mocked(tasksApi.getTaskGeneratedMessages).mockImplementation(async () => persistedHistory)
+    vi.mocked(tasksApi.deleteTaskGeneratedMessage).mockImplementation(async (_taskId, messageId) => {
+      persistedHistory = persistedHistory.filter((message) => message.id !== messageId)
+    })
     mockNavigate.mockClear()
   })
 
@@ -93,7 +106,18 @@ describe('EditTaskPage', () => {
   })
 
   it('should_generatePreviewAndUpdateTask_when_formSubmitted', async () => {
-    vi.mocked(tasksApi.generateTaskPreview).mockResolvedValue('SUBJECT: Preview\nBODY:\nFormal nonsense')
+    vi.mocked(tasksApi.generateTaskPreview).mockImplementation(async () => {
+      const content = 'SUBJECT: Preview\nBODY:\nFormal nonsense'
+      const nextMessage = {
+        id: `message-${persistedHistory.length + 1}`,
+        taskId: 'task-1',
+        label: `Message #${persistedHistory.length + 1}`,
+        content,
+        createdAt: '2026-03-27T12:00:00Z',
+      }
+      persistedHistory = [nextMessage, ...persistedHistory]
+      return content
+    })
     vi.mocked(tasksApi.updateTask).mockResolvedValue({
       ...mockTask,
       name: 'Daily Check-in',
@@ -137,7 +161,8 @@ describe('EditTaskPage', () => {
           emailLookback: 'last_day',
         })
       )
-      expect(vi.mocked(tasksApi.generateTaskPreview).mock.calls[0][0]).toEqual(
+      expect(vi.mocked(tasksApi.generateTaskPreview).mock.calls[0][0]).toEqual('task-1')
+      expect(vi.mocked(tasksApi.generateTaskPreview).mock.calls[0][1]).toEqual(
         expect.objectContaining({
           entity: mockEntity,
           task: expect.objectContaining({
@@ -201,8 +226,34 @@ describe('EditTaskPage', () => {
 
   it('should_showAndManageGeneratedMessageHistory_when_multipleMessagesGenerated', async () => {
     vi.mocked(tasksApi.generateTaskPreview)
-      .mockResolvedValueOnce('SUBJECT: First\nBODY:\nFirst output')
-      .mockResolvedValueOnce('SUBJECT: Second\nBODY:\nSecond output')
+      .mockImplementationOnce(async () => {
+        const content = 'SUBJECT: First\nBODY:\nFirst output'
+        persistedHistory = [
+          {
+            id: 'message-1',
+            taskId: 'task-1',
+            label: 'Message #1',
+            content,
+            createdAt: '2026-03-27T12:00:00Z',
+          },
+          ...persistedHistory,
+        ]
+        return content
+      })
+      .mockImplementationOnce(async () => {
+        const content = 'SUBJECT: Second\nBODY:\nSecond output'
+        persistedHistory = [
+          {
+            id: 'message-2',
+            taskId: 'task-1',
+            label: 'Message #2',
+            content,
+            createdAt: '2026-03-27T12:10:00Z',
+          },
+          ...persistedHistory,
+        ]
+        return content
+      })
 
     renderPage()
     await screen.findByRole('link', { name: /back to entity a/i })
@@ -215,7 +266,7 @@ describe('EditTaskPage', () => {
     fireEvent.click(generateButton)
 
     await waitFor(() => {
-      expect(screen.getByText(/Second output/i)).toBeInTheDocument()
+      expect(tasksApi.generateTaskPreview).toHaveBeenCalledTimes(2)
     })
 
     const history = screen.getByRole('list', { name: /generated message history/i })
@@ -224,6 +275,9 @@ describe('EditTaskPage', () => {
     const firstMessageHistoryItem = screen.getByRole('button', { name: /^message #1$/i })
     const secondMessageHistoryItem = screen.getByRole('button', { name: /^message #2$/i })
 
+    fireEvent.click(secondMessageHistoryItem)
+    expect(screen.getByText(/Second output/i)).toBeInTheDocument()
+
     fireEvent.click(firstMessageHistoryItem)
     expect(screen.getByText(/First output/i)).toBeInTheDocument()
 
@@ -234,11 +288,29 @@ describe('EditTaskPage', () => {
     )
 
     await waitFor(() => {
+      expect(tasksApi.deleteTaskGeneratedMessage).toHaveBeenCalledWith('task-1', 'message-1')
       expect(firstMessageHistoryItem).not.toBeInTheDocument()
       expect(secondMessageHistoryItem).toBeInTheDocument()
     })
   })
 
+  it('should_loadPersistedGeneratedMessageHistory_when_pageLoads', async () => {
+    persistedHistory = [
+      {
+        id: 'message-1',
+        taskId: 'task-1',
+        label: 'Message #1',
+        content: 'SUBJECT: Persisted\nBODY:\nFrom storage',
+        createdAt: '2026-03-27T12:00:00Z',
+      },
+    ]
+
+    renderPage()
+
+    await screen.findByRole('button', { name: /^message #1$/i })
+    expect(screen.getByText(/From storage/i)).toBeInTheDocument()
+  })
+
   it('should_renderActivateButton_when_taskIsInactive', async () => {
     renderPage({ task: { ...mockTask, active: false } })