CI: experimental flake-update workflow

I want to use a matrix strategy for the check and cachix workflows, so I
need to not just commit but also push the updated flake.lock somewhere
other than `main`, so multiple workers can check out the pending change.

Try the simplest possible thing first, expecting it to fail with
permission issues.

.github/workflows/flake-update.yml

@@ -0,0 +1,39 @@
+# Copyright 2024 Google LLC
+#
+# Licensed under the Apache License, Version 2.0 (the "License");
+# you may not use this file except in compliance with the License.
+# You may obtain a copy of the License at
+#
+#     http://www.apache.org/licenses/LICENSE-2.0
+#
+# Unless required by applicable law or agreed to in writing, software
+# distributed under the License is distributed on an "AS IS" BASIS,
+# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+# See the License for the specific language governing permissions and
+# limitations under the License.
+
+name: nix flake update
+description: "Check out main, update flake.lock, push to flake-update."
+
+on:
+  workflow_dispatch:
+
+jobs:
+  check:
+    runs-on: ubuntu-latest
+    permissions:
+      contents: "write"
+    steps:
+      - name: Check out repository
+        uses: actions/checkout@v4
+        with:
+          ref: main
+      - name: Install Nix
+        uses: DeterminateSystems/nix-installer-action@main
+      - name: Update and push flake.lock
+        run: |
+          git config user.email "github-actions[bot]@users.noreply.github.com"
+          git config user.name "github-actions[bot]"
+          git checkout -b flake-update
+          nix flake update --commit-lock-file
+          git push --force origin flake-update