fix: commit pre-compiled dist and simplify sync Dockerfile

Server npm proxy silently drops devDependencies, making TypeScript
unavailable in Docker. Solution: compile locally and commit dist/.
Dockerfile now only needs prod deps + Playwright, both of which
install cleanly via the public registry.

Also fix TS2688/TS2304 errors: add DOM to tsconfig lib and cast
querySelectorAll results to Element inside $$eval callbacks.

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

sync/Dockerfile

@@ -1,19 +1,11 @@
-# Stage 1: build TypeScript
-FROM node:20-slim AS builder
-WORKDIR /app
-RUN npm install -g typescript --registry https://registry.npmjs.org
-COPY package.json package-lock.json ./
-RUN npm install --registry https://registry.npmjs.org
-COPY tsconfig.json ./
-COPY src ./src
-RUN tsc && npm prune --production --registry https://registry.npmjs.org
-
-# Stage 2: runtime with Playwright
+# dist/ is compiled locally and committed to the repo.
+# The server npm proxy blocks devDependency installs inside Docker.
 FROM mcr.microsoft.com/playwright:v1.47.0-jammy
 WORKDIR /app
 RUN npx playwright install chromium --with-deps
-COPY --from=builder /app/node_modules ./node_modules
-COPY --from=builder /app/dist ./dist
+COPY package.json package-lock.json ./
+RUN npm install --omit=dev --registry https://registry.npmjs.org
+COPY dist ./dist
 
 CMD ["node", "dist/index.js"]