feat: embed frontend into backend server with full-stack build pipeline (RCA-20)

The backend now serves the Vue admin UI as static files with SPA fallback,
eliminating the need for a separate web server. Dockerfile builds both
frontend and backend in a multi-stage pipeline. Added build:web and
build:all scripts, updated CI to verify frontend builds, and fixed
vitest config to exclude Playwright tests.

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

.github/workflows/ci.yml

@@ -24,9 +24,26 @@ jobs:
       - run: npm run typecheck
       - run: npm test
 
+  web:
+    runs-on: ubuntu-latest
+    steps:
+      - uses: actions/checkout@v4
+
+      - uses: actions/setup-node@v4
+        with:
+          node-version: 22
+          cache: npm
+          cache-dependency-path: web/package-lock.json
+
+      - name: Install and build frontend
+        working-directory: web
+        run: |
+          npm ci
+          npm run build
+
   docker:
     runs-on: ubuntu-latest
-    needs: test
+    needs: [test, web]
     steps:
       - uses: actions/checkout@v4
 
@@ -38,6 +55,7 @@ jobs:
           docker run -d --name cb-test -p 8080:8080 cookiebridge:ci
           sleep 3
           curl -sf http://localhost:8080/health
+          curl -sf http://localhost:8080/ | grep -q '<div id="app">'
           docker stop cb-test
 
   extension: