Add PostgreSQL compatibility matrix CI workflow

Introduced a GitHub Actions workflow to verify compatibility with PostgreSQL versions 14 through 18. Implemented a smoke test script to check core database metrics and version-specific differences. Updated the README with details about the compatibility matrix and usage instructions for the script.

.github/workflows/pg-compat-matrix.yml

@@ -0,0 +1,47 @@
+name: PostgreSQL Compatibility Matrix
+
+on:
+  push:
+    branches: ["main", "master"]
+  pull_request:
+
+jobs:
+  pg-compat:
+    name: PG${{ matrix.pg_version }} smoke
+    runs-on: ubuntu-latest
+    strategy:
+      fail-fast: false
+      matrix:
+        pg_version: ["14", "15", "16", "17", "18"]
+
+    services:
+      postgres:
+        image: postgres:${{ matrix.pg_version }}
+        env:
+          POSTGRES_DB: compatdb
+          POSTGRES_USER: postgres
+          POSTGRES_PASSWORD: postgres
+        ports:
+          - 5432:5432
+        options: >-
+          --health-cmd "pg_isready -U postgres -d compatdb"
+          --health-interval 5s
+          --health-timeout 5s
+          --health-retries 20
+
+    steps:
+      - name: Checkout
+        uses: actions/checkout@v4
+
+      - name: Set up Python
+        uses: actions/setup-python@v5
+        with:
+          python-version: "3.12"
+
+      - name: Install backend dependencies
+        run: pip install -r backend/requirements.txt
+
+      - name: Run PostgreSQL compatibility smoke checks
+        env:
+          PG_DSN: postgresql://postgres:postgres@127.0.0.1:5432/compatdb?sslmode=disable
+        run: python backend/scripts/pg_compat_smoke.py