fix: serve chat-widget.js correctly in production

- Copy product/ into Docker image (was missing from final stage)
- Fix static file path: ../../product → ../product (wrong depth from dist/index.js)
- Add ANTHROPIC_API_KEY to K8s manifest (chat endpoint was returning 500)

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

Dockerfile

@@ -1,6 +1,7 @@
 FROM node:20-alpine AS builder
 WORKDIR /app
 COPY package*.json ./
+COPY scripts/ ./scripts/
 RUN npm install
 COPY tsconfig.json ./
 COPY src/ ./src/
@@ -9,7 +10,9 @@ RUN npx tsc
 FROM node:20-alpine
 WORKDIR /app
 COPY package*.json ./
+COPY scripts/ ./scripts/
 RUN npm install --omit=dev
 COPY --from=builder /app/dist ./dist
+COPY product/ ./product/
 EXPOSE 3456
 CMD ["node", "dist/index.js"]