chore(repo): restructure as monorepo with server and client workspaces

- move NestJS app into server/ subdirectory
- add client/ React+TypeScript (Vite) app with Hello World
- update docker-compose to build and run both services
- add root package.json declaring npm workspaces
- update .gitignore to cover node_modules and dist at all depths

server/Dockerfile

@@ -0,0 +1,39 @@
+# ── Build stage ──────────────────────────────────────────────────────────────
+FROM node:22-slim AS builder
+
+WORKDIR /app
+
+COPY package*.json ./
+RUN npm ci
+
+COPY nest-cli.json tsconfig*.json ./
+COPY src ./src
+RUN npm run build
+
+# ── Runtime stage ─────────────────────────────────────────────────────────────
+FROM node:22-slim AS runtime
+
+# Playwright / Chromium system dependencies
+RUN apt-get update && apt-get install -y --no-install-recommends \
+    chromium \
+    fonts-noto \
+    ca-certificates \
+    && rm -rf /var/lib/apt/lists/*
+
+# Tell Playwright to use the system Chromium instead of downloading its own
+ENV PLAYWRIGHT_SKIP_BROWSER_DOWNLOAD=1
+ENV PLAYWRIGHT_CHROMIUM_EXECUTABLE_PATH=/usr/bin/chromium
+
+WORKDIR /app
+
+COPY package*.json ./
+RUN npm ci --omit=dev
+
+COPY --from=builder /app/dist ./dist
+
+# Runtime directories (keys and SQLite DB mounted via volumes)
+RUN mkdir -p data keys
+
+EXPOSE 3000
+
+CMD ["node", "dist/main"]