feat: add GitHub Actions workflow for backend formatting and testing

.github/workflows/backend-format.yml

@@ -0,0 +1,52 @@
+name: Backend Format
+
+on:
+    pull_request:
+        paths:
+            - "backend/**"
+            - "scripts/**"
+            - "pyproject.toml"
+            - ".github/workflows/backend-format.yml"
+
+jobs:
+    format:
+        runs-on: ubuntu-latest
+
+        steps:
+            - name: Check out repository
+              uses: actions/checkout@v4
+
+            - name: Set up Python
+              uses: actions/setup-python@v5
+              with:
+                  python-version: "3.10"
+
+            - name: Install dependencies
+              run: |
+                  python -m pip install --upgrade pip
+                  python -m venv .venv
+                  source .venv/bin/activate
+                  pip install -e .[dev]
+
+            - name: Run black
+              run: |
+                  source .venv/bin/activate
+                  black backend
+
+            - name: Run isort
+              run: |
+                  source .venv/bin/activate
+                  isort backend
+
+            - name: Run pytest
+              run: |
+                  source .venv/bin/activate
+                  pytest backend/tests
+
+            - name: Upload formatting diff
+              if: failure()
+              uses: actions/upload-artifact@v4
+              with:
+                  name: backend-formatting-diff
+                  path: |
+                      backend