[taskboard] add completion sync APIs

app/api/tasks/[id]/callback/route.ts

@@ -0,0 +1,30 @@
+import { NextResponse } from "next/server";
+
+import { applyTaskCallback } from "@/lib/tasks";
+
+export async function POST(
+  request: Request,
+  { params }: { params: Promise<{ id: string }> },
+) {
+  const { id } = await params;
+  const numericId = Number(id);
+  if (!Number.isInteger(numericId) || numericId <= 0) {
+    return NextResponse.json({ error: "invalid_task_id" }, { status: 400 });
+  }
+
+  const payload = (await request.json()) as {
+    status?: "Backlog" | "Todo" | "In Progress" | "Review" | "Done";
+    dispatch_state?: "planned" | "assigned" | "dispatched" | "acknowledged" | "completed" | "failed";
+    summary?: string | null;
+    detail?: string | null;
+    completed_by?: string | null;
+    last_error?: string | null;
+  };
+
+  const updated = await applyTaskCallback(numericId, payload);
+  if (!updated) {
+    return NextResponse.json({ error: "task_not_found" }, { status: 404 });
+  }
+
+  return NextResponse.json(updated);
+}