Add backlog audit and task update command

- agents/prompts/backlog_audit.md: QA analyst prompt for checking
  which pending tasks are already implemented in the codebase
- agents/runner.py: run_audit() — project-level agent that reads
  all pending tasks, inspects code, returns classification
- cli/main.py: kin audit <project_id> — runs audit, offers to mark
  done tasks; kin task update <id> --status --priority
- web/api.py: POST /api/projects/{id}/audit (runs audit inline),
  POST /api/projects/{id}/audit/apply (batch mark as done)
- Frontend: "Audit backlog" button on ProjectView with results
  modal showing already_done/still_pending/unclear categories

Co-Authored-By: Claude Opus 4.6 <noreply@anthropic.com>

web/frontend/src/views/ProjectView.vue

@@ -1,6 +1,6 @@
 <script setup lang="ts">
 import { ref, onMounted, computed } from 'vue'
-import { api, type ProjectDetail } from '../api'
+import { api, type ProjectDetail, type AuditResult } from '../api'
 import Badge from '../components/Badge.vue'
 import Modal from '../components/Modal.vue'
 
@@ -28,6 +28,42 @@ function toggleMode() {
   localStorage.setItem(`kin-mode-${props.id}`, autoMode.value ? 'auto' : 'review')
 }
 
+// Audit
+const auditLoading = ref(false)
+const auditResult = ref<AuditResult | null>(null)
+const showAuditModal = ref(false)
+const auditApplying = ref(false)
+
+async function runAudit() {
+  auditLoading.value = true
+  auditResult.value = null
+  try {
+    const res = await api.auditProject(props.id)
+    auditResult.value = res
+    showAuditModal.value = true
+  } catch (e: any) {
+    error.value = e.message
+  } finally {
+    auditLoading.value = false
+  }
+}
+
+async function applyAudit() {
+  if (!auditResult.value?.already_done?.length) return
+  auditApplying.value = true
+  try {
+    const ids = auditResult.value.already_done.map(t => t.id)
+    await api.auditApply(props.id, ids)
+    showAuditModal.value = false
+    auditResult.value = null
+    await load()
+  } catch (e: any) {
+    error.value = e.message
+  } finally {
+    auditApplying.value = false
+  }
+}
+
 // Add task modal
 const showAddTask = ref(false)
 const taskForm = ref({ title: '', priority: 5, route_type: '' })
@@ -216,6 +252,12 @@ async function addDecision() {
             :title="autoMode ? 'Auto mode: agents can write files' : 'Review mode: agents read-only'">
             {{ autoMode ? '&#x1F513; Auto' : '&#x1F512; Review' }}
           </button>
+          <button @click="runAudit" :disabled="auditLoading"
+            class="px-2 py-1 text-xs bg-purple-900/30 text-purple-400 border border-purple-800 rounded hover:bg-purple-900/50 disabled:opacity-50"
+            title="Check which pending tasks are already done">
+            <span v-if="auditLoading" class="inline-block w-3 h-3 border-2 border-purple-400 border-t-transparent rounded-full animate-spin mr-1"></span>
+            {{ auditLoading ? 'Auditing...' : 'Audit backlog' }}
+          </button>
           <button @click="showAddTask = true"
             class="px-3 py-1 text-xs bg-gray-800 text-gray-300 border border-gray-700 rounded hover:bg-gray-700">
             + Task
@@ -350,5 +392,46 @@ async function addDecision() {
         </button>
       </form>
     </Modal>
+
+    <!-- Audit Modal -->
+    <Modal v-if="showAuditModal && auditResult" title="Backlog Audit Results" @close="showAuditModal = false">
+      <div v-if="!auditResult.success" class="text-red-400 text-sm">
+        Audit failed: {{ auditResult.error }}
+      </div>
+      <div v-else class="space-y-4">
+        <div v-if="auditResult.already_done?.length">
+          <h3 class="text-sm font-semibold text-green-400 mb-2">Already done ({{ auditResult.already_done.length }})</h3>
+          <div v-for="item in auditResult.already_done" :key="item.id"
+            class="px-3 py-2 border border-green-900/50 rounded text-xs mb-1">
+            <span class="text-green-400 font-medium">{{ item.id }}</span>
+            <span class="text-gray-400 ml-2">{{ item.reason }}</span>
+          </div>
+        </div>
+        <div v-if="auditResult.still_pending?.length">
+          <h3 class="text-sm font-semibold text-gray-400 mb-2">Still pending ({{ auditResult.still_pending.length }})</h3>
+          <div v-for="item in auditResult.still_pending" :key="item.id"
+            class="px-3 py-2 border border-gray-800 rounded text-xs mb-1">
+            <span class="text-gray-300 font-medium">{{ item.id }}</span>
+            <span class="text-gray-500 ml-2">{{ item.reason }}</span>
+          </div>
+        </div>
+        <div v-if="auditResult.unclear?.length">
+          <h3 class="text-sm font-semibold text-yellow-400 mb-2">Unclear ({{ auditResult.unclear.length }})</h3>
+          <div v-for="item in auditResult.unclear" :key="item.id"
+            class="px-3 py-2 border border-yellow-900/50 rounded text-xs mb-1">
+            <span class="text-yellow-400 font-medium">{{ item.id }}</span>
+            <span class="text-gray-400 ml-2">{{ item.reason }}</span>
+          </div>
+        </div>
+        <div v-if="auditResult.cost_usd || auditResult.duration_seconds" class="text-xs text-gray-600">
+          <span v-if="auditResult.duration_seconds">{{ auditResult.duration_seconds }}s</span>
+          <span v-if="auditResult.cost_usd" class="ml-2">${{ auditResult.cost_usd?.toFixed(4) }}</span>
+        </div>
+        <button v-if="auditResult.already_done?.length" @click="applyAudit" :disabled="auditApplying"
+          class="w-full py-2 bg-green-900/50 text-green-400 border border-green-800 rounded text-sm hover:bg-green-900 disabled:opacity-50">
+          {{ auditApplying ? 'Applying...' : `Mark ${auditResult.already_done.length} tasks as done` }}
+        </button>
+      </div>
+    </Modal>
   </div>
 </template>