chore: added update flake workflow, build workflow

.gitea/workflows/build-after-flake-update.yml

@@ -0,0 +1,29 @@
+name: Build (nix)
+
+on:
+  workflow_run:
+    workflows:
+      - Update flake lock
+    types:
+      - completed
+
+permissions:
+  contents: read
+
+jobs:
+  build:
+    if: ${{ gitea.event.workflow_run.conclusion == 'success' }}
+    runs-on: ubuntu-latest
+
+    steps:
+      - name: Check out repository
+        uses: actions/checkout@v4
+        with:
+          # The update workflow may have pushed a newer flake.lock commit.
+          ref: ${{ gitea.event.workflow_run.head_branch }}
+
+      - name: Install upstream Nix
+        uses: cachix/install-nix-action@v31
+
+      - name: Build flake
+        run: nix build

.gitea/workflows/update-flake-lock.yml

@@ -0,0 +1,40 @@
+name: Update flake lock
+
+on:
+  schedule:
+    # Gitea cron schedules use UTC. 07:00 UTC is 03:00 EDT.
+    - cron: "0 7 * * 0"
+  workflow_dispatch:
+
+permissions:
+  contents: write
+
+jobs:
+  update-flake-lock:
+    runs-on: ubuntu-latest
+
+    steps:
+      - name: Check out repository
+        uses: actions/checkout@v4
+
+      - name: Install upstream Nix
+        uses: cachix/install-nix-action@v31
+
+      - name: Update flake lock
+        run: nix flake update
+
+      - name: Commit and push changes
+        shell: bash
+        run: |
+          set -euo pipefail
+
+          if git diff --quiet -- flake.lock; then
+            echo "flake.lock is already up to date"
+            exit 0
+          fi
+
+          git config user.name "gitea-actions[bot]"
+          git config user.email "gitea-actions[bot]@noreply.localhost"
+          git add flake.lock
+          git commit -m "chore: update flake lock"
+          git push