chore: add sync config (#3860)

.github/sync.yml

@@ -0,0 +1,5 @@
+nextauthjs/next-auth-example-sync-test@main:
+  - .github/FUNDING.yml
+  - source: apps/example
+      dest: .
+      deleteOrphaned: true

.github/workflows/sync-example.yml

@@ -0,0 +1,16 @@
+name: Sync Example Repository
+on:
+  push:
+    branches:
+      - main
+  workflow_dispatch:
+jobs:
+  sync:
+    runs-on: ubuntu-latest
+    steps:
+      - name: Checkout Repository
+        uses: actions/checkout@v2
+      - name: Run GitHub File Sync
+        uses: BetaHuhn/repo-file-sync-action@v1
+        with:
+          GH_PAT: ${{ secrets.SYNC_EXAMPLE_PAT }}