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>

CONTRIBUTING.md

@@ -22,6 +22,23 @@ npm test          # Run test suite
 npm run typecheck # Type checking only
 ```
 
+**Admin panel (frontend):**
+
+```bash
+cd web
+npm install
+npm run dev       # Starts Vite dev server on :5173 (proxies API to backend)
+```
+
+The frontend dev server proxies `/api`, `/admin`, `/ws`, and `/health` to `http://localhost:8100`. Start the backend first with `npm run dev` (or adjust the proxy target in `web/vite.config.ts`).
+
+**Full production build:**
+
+```bash
+npm run build:all   # Builds backend (tsc) + frontend (vite) → copies to public/
+npm start           # Serves everything on :8080
+```
+
 **Extension:**
 
 ```bash