feat(insights): add getBacklogHealth helper — stuck tasks + missing AC/plan counts (#48)

Three read-only counters: stories without acceptance_criteria, tasks without
implementation_plan, and top-10 IN_PROGRESS tasks stuck >7 days. All scoped
via productAccessFilter.

Co-authored-by: Claude Sonnet 4.6 <noreply@anthropic.com>

lib/insights/backlog-health.ts

@@ -0,0 +1,69 @@
+import { prisma } from '@/lib/prisma'
+import { productAccessFilter } from '@/lib/product-access'
+
+export interface StuckTask {
+  taskId: string
+  title: string
+  productId: string
+  productName: string
+  sprintGoal: string | null
+  daysStuck: number
+  updatedAt: string
+}
+
+export interface BacklogHealth {
+  storiesWithoutAc: number
+  tasksWithoutPlan: number
+  stuckTasks: StuckTask[]
+}
+
+const SEVEN_DAYS_MS = 7 * 86_400_000
+
+export async function getBacklogHealth(userId: string): Promise<BacklogHealth> {
+  const now = new Date()
+  const stuckCutoff = new Date(now.getTime() - SEVEN_DAYS_MS)
+
+  const [storiesWithoutAc, tasksWithoutPlan, rawStuck] = await Promise.all([
+    prisma.story.count({
+      where: {
+        OR: [{ acceptance_criteria: null }, { acceptance_criteria: '' }],
+        product: productAccessFilter(userId),
+      },
+    }),
+    prisma.task.count({
+      where: {
+        implementation_plan: null,
+        story: { product: productAccessFilter(userId) },
+      },
+    }),
+    prisma.task.findMany({
+      where: {
+        status: 'IN_PROGRESS',
+        updated_at: { lt: stuckCutoff },
+        story: { product: productAccessFilter(userId) },
+      },
+      orderBy: { updated_at: 'asc' },
+      take: 10,
+      include: {
+        story: {
+          include: {
+            product: { select: { id: true, name: true } },
+            sprint: { select: { sprint_goal: true } },
+          },
+        },
+      },
+    }),
+  ])
+
+  const stuckTasks: StuckTask[] = rawStuck.map(t => ({
+    taskId: t.id,
+    title: t.title,
+    productId: t.story.product.id,
+    productName: t.story.product.name,
+    sprintGoal: t.story.sprint?.sprint_goal ?? null,
+    daysStuck: Math.floor((now.getTime() - t.updated_at.getTime()) / 86_400_000),
+    updatedAt: t.updated_at.toISOString(),
+  }))
+
+  return { storiesWithoutAc, tasksWithoutPlan, stuckTasks }
+}