feat: Implement Alembic database migrations

.github/workflows/migration-check.yml

@@ -0,0 +1,41 @@
+name: Migration Check
+
+on:
+  pull_request:
+    branches: [main]
+    paths:
+      - 'backend/**'
+
+jobs:
+  check-migrations:
+    runs-on: ubuntu-latest
+    steps:
+      - uses: actions/checkout@v4
+
+      - name: Setup Python
+        uses: actions/setup-python@v5
+        with:
+          python-version: '3.12'
+
+      - name: Install just
+        uses: extractions/setup-just@v2
+
+      - name: Install uv
+        uses: astral-sh/setup-uv@v4
+
+      - name: Install dependencies
+        run: |
+          cd backend
+          uv pip install -e . --system
+
+      - name: Check for multiple heads
+        run: |
+          cd backend
+          just check
+
+      - name: Test fresh install
+        run: |
+          cd backend
+          rm -f /tmp/ci_test.db
+          SQLITE_DB_PATH=/tmp/ci_test.db just upgrade
+          echo "Fresh install migration succeeded"