feat(ST-1112): wire TaskDialog into sprint page via searchParams

Sprint page now reads ?newTask, ?storyId, and ?editTask query params.
For edit mode: fetches the task server-side with productAccessFilter
scope (invalid/foreign IDs redirect to closePath). Renders TaskDialog
when either param is present. closePath is the sprint route without
query params.

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

app/(app)/products/[id]/sprint/page.tsx

@@ -1,19 +1,29 @@
 import { notFound, redirect } from 'next/navigation'
 import { getSession } from '@/lib/auth'
 import { getAccessibleProduct } from '@/lib/product-access'
+import { productAccessFilter } from '@/lib/product-access'
 import { prisma } from '@/lib/prisma'
 import { SprintBoardClient } from '@/components/sprint/sprint-board-client'
 import { SprintHeader } from '@/components/sprint/sprint-header'
 import type { SprintStory, PbiWithStories, ProductMember } from '@/components/sprint/sprint-backlog'
 import type { Task } from '@/components/sprint/task-list'
+import { TaskDialog } from '@/app/_components/tasks/task-dialog'
+import type { TaskDialogTask } from '@/app/_components/tasks/task-dialog'
 import Link from 'next/link'
 
 interface Props {
   params: Promise<{ id: string }>
+  searchParams: Promise<{
+    newTask?: string
+    storyId?: string
+    editTask?: string
+  }>
 }
 
-export default async function SprintBoardPage({ params }: Props) {
+export default async function SprintBoardPage({ params, searchParams }: Props) {
   const { id } = await params
+  const { newTask, storyId: storyIdParam, editTask } = await searchParams
+
   const session = await getSession()
   if (!session.userId) redirect('/login')
 
@@ -104,6 +114,31 @@ export default async function SprintBoardPage({ params }: Props) {
 
   const sprintStoryIdList = sprintStories.map(s => s.id)
   const isDemo = session.isDemo ?? false
+  const closePath = `/products/${id}/sprint`
+
+  // Fetch task for edit mode (auth-scoped)
+  let editTaskData: TaskDialogTask | null = null
+  if (editTask) {
+    const t = await prisma.task.findFirst({
+      where: {
+        id: editTask,
+        story: { product: productAccessFilter(session.userId) },
+      },
+      select: {
+        id: true,
+        title: true,
+        description: true,
+        implementation_plan: true,
+        priority: true,
+        status: true,
+        created_at: true,
+      },
+    })
+    if (!t) redirect(closePath)
+    editTaskData = t
+  }
+
+  const showDialog = !!newTask || !!editTaskData
 
   return (
     <div className="flex flex-col h-full">
@@ -134,6 +169,16 @@ export default async function SprintBoardPage({ params }: Props) {
           ← Product Backlog
         </Link>
       </div>
+
+      {showDialog && (
+        <TaskDialog
+          task={editTaskData ?? undefined}
+          storyId={storyIdParam}
+          productId={id}
+          closePath={closePath}
+          isDemo={isDemo}
+        />
+      )}
     </div>
   )
 }