chore: add flake update automation

This is used for testing updates and gauging how up-to-date my config
is. In case of failure, it should not update it.

.github/workflows/automate-update.yml

@@ -0,0 +1,32 @@
+name: "Automated flake inputs update"
+on:
+  schedule:
+    # Every week on Friday.
+    - cron: '0 * * * 5'
+jobs:
+  build:
+    runs-on: ubuntu-latest
+    steps:
+      - uses: actions/checkout@v3
+      - uses: cachix/install-nix-action@v16
+        with:
+          nix_path: nixpkgs=channel:nixos-unstable
+      - name: Update flake inputs
+        run: |
+          nix shell nixpkgs#git
+
+          # This is set by the GitHub Actions bot just to make identifying which commits are automated.
+          git config user.name 'github-actions[bot]'
+          git config user.email 'github-actions[bot]@users.noreply.github.com'
+
+          nix flake update --commit-lock-file \
+            --commit-lockfile-summary 'flake.lock: update-inputs'
+      - name: Build custom packages
+        run: nix shell nixpkgs#nix-build-uncached --command nix-build-uncached ./pkgs
+      - name: Build NixOS configurations
+        run: nix build .#nixosConfigurations.ni.config.system.build.toplevel
+      - name: Push updates to remote
+        run: |
+          git remote remove origin
+          git remote add origin https://${{ secrets.GITHUB_TOKEN }}@github.com/foo-dogsquared/nixos-config.git
+          git push --set-upstream origin master --tags