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>

vitest.config.ts

@@ -4,5 +4,6 @@ export default defineConfig({
   test: {
     globals: true,
     testTimeout: 15_000,
+    exclude: ["node_modules", "dist", "web", "extension"],
   },
 });