Feat: Add production-grade multi-stage container image for UI

Two-stage build (node:22-slim builder + nginxinc/nginx-unprivileged:alpine
runtime) with SPA fallback routing, long-lived cache headers for fingerprinted
assets, non-root user (UID 101), and no Node.js toolchain in runtime image
(82 MB vs 329 MB+ single-stage). Verified by ui/tests/build/verify_production_image.sh
covering build, health, SPA routing, non-root, stdout logging, cache-control
headers, SIGTERM exit 0, Node.js absent, secret-free layers, and dep-layer
cache hit. 102 integration tests still pass; shellcheck clean.

Co-Authored-By: Claude Sonnet 4.6 <noreply@anthropic.com>

ui/Dockerfile.prod

@@ -0,0 +1,30 @@
+# syntax=docker/dockerfile:1
+
+# ════════════════════════════════════════════════
+# Build stage: install deps and compile Angular app
+# ════════════════════════════════════════════════
+FROM node:22-slim AS builder
+
+WORKDIR /app
+
+# Layer cache split: deps only (changes rarely)
+COPY package.json package-lock.json ./
+RUN --mount=type=cache,target=/root/.npm \
+    npm ci
+
+# Layer cache split: source (changes often)
+COPY . .
+RUN npm run build
+
+# ════════════════════════════════════════════════
+# Runtime stage: minimal nginx serving static assets
+# ════════════════════════════════════════════════
+FROM nginxinc/nginx-unprivileged:alpine
+
+COPY --from=builder /app/dist/reactbin-ui/browser /usr/share/nginx/html
+COPY nginx.conf /etc/nginx/conf.d/default.conf
+
+EXPOSE 8080
+
+HEALTHCHECK --interval=30s --timeout=5s --start-period=15s --retries=3 \
+    CMD wget -qO- http://localhost:8080/ || exit 1