feat(e2e): add Playwright E2E testing infrastructure and critical path tests

Set up Playwright with dual-project config (API + Web), auth test fixtures,
16 E2E tests covering registration, login, profile, token refresh, and
homepage rendering. Added GitHub Actions CI workflow for automated E2E runs.

Co-Authored-By: Paperclip <noreply@paperclip.ing>

.github/workflows/e2e.yml

@@ -0,0 +1,75 @@
+name: E2E Tests
+
+on:
+  push:
+    branches: [main]
+  pull_request:
+    branches: [main]
+
+concurrency:
+  group: e2e-${{ github.ref }}
+  cancel-in-progress: true
+
+jobs:
+  e2e:
+    name: Playwright E2E
+    runs-on: ubuntu-latest
+    timeout-minutes: 15
+
+    services:
+      postgres:
+        image: postgis/postgis:16-3.4
+        env:
+          POSTGRES_DB: goodgo_test
+          POSTGRES_USER: goodgo
+          POSTGRES_PASSWORD: goodgo_test_secret
+        ports:
+          - 5432:5432
+        options: >-
+          --health-cmd "pg_isready -U goodgo -d goodgo_test"
+          --health-interval 10s
+          --health-timeout 5s
+          --health-retries 5
+          --health-start-period 30s
+
+    env:
+      DATABASE_URL: postgresql://goodgo:goodgo_test_secret@localhost:5432/goodgo_test
+      NODE_ENV: test
+      JWT_SECRET: e2e-test-jwt-secret-key
+      JWT_REFRESH_SECRET: e2e-test-refresh-secret-key
+
+    steps:
+      - name: Checkout
+        uses: actions/checkout@v4
+
+      - name: Install pnpm
+        uses: pnpm/action-setup@v4
+
+      - name: Setup Node.js
+        uses: actions/setup-node@v4
+        with:
+          node-version: 22
+          cache: pnpm
+
+      - name: Install dependencies
+        run: pnpm install --frozen-lockfile
+
+      - name: Install Playwright browsers
+        run: npx playwright install --with-deps chromium
+
+      - name: Run database migrations
+        run: pnpm db:migrate:deploy
+
+      - name: Build apps
+        run: pnpm build
+
+      - name: Run E2E tests
+        run: pnpm test:e2e
+
+      - name: Upload test report
+        if: ${{ !cancelled() }}
+        uses: actions/upload-artifact@v4
+        with:
+          name: playwright-report
+          path: playwright-report/
+          retention-days: 14