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>

package.json

@@ -6,6 +6,8 @@
   "types": "dist/index.d.ts",
   "scripts": {
     "build": "tsc",
+    "build:web": "cd web && npm run build && cd .. && rm -rf public && cp -r web/dist public",
+    "build:all": "npm run build && npm run build:web",
     "start": "tsx src/cli.ts",
     "dev": "tsx --watch src/cli.ts",
     "test": "vitest run",