ci: auto-merge flake updates to example/simple

Notes on how the Github App was created and configured:
https://nixos.zulipchat.com/#narrow/stream/413950-nix/topic/.60flake.2Elock.60.20auto-merge.20on.20GitHub/near/440987146

.github/workflows/update-flake-lock-ex-simple.yaml

@@ -8,16 +8,33 @@ jobs:
   example-lock:
     runs-on: ubuntu-latest
     steps:
+      - name: Generate Github App Token
+        uses: navikt/github-app-token-generator@v1
+        id: github-app-token
+        with:
+          app-id: ${{ vars.NIXOS_ASIA_APP_ID }}
+          private-key: ${{ secrets.NIXOS_ASIA_PRIVATE_KEY }}
       - name: Checkout repository
         uses: actions/checkout@v4
       - name: Install Nix
         uses: DeterminateSystems/nix-installer-action@main
       - name: Update flake.lock
         uses: DeterminateSystems/update-flake-lock@main
+        id: update-flake-lock
         with:
           commit-msg: "chore(example): Update simple/flake.lock"
           pr-title: "Update example/simple/flake.lock"
+          pr-body: |
+            Automated changes by the [update-flake-lock](https://github.com/DeterminateSystems/update-flake-lock) GitHub Action.
+
+            ```
+            {{ env.GIT_COMMIT_MESSAGE }}
+            ```
           pr-labels: |
             automated
           path-to-flake-dir: 'example/simple'
-          branch: "update_flake_lock_ex_simple"
+          branch: "update_flake_lock_ex_simple"
+          token: ${{ steps.github-app-token.outputs.token }}
+      - run: "gh pr merge --auto --rebase ${{ steps.update-flake-lock.outputs.pull-request-number }}"
+        env:
+          GH_TOKEN: ${{ github.token }