Fix final-review findings for Playwright fallback

- server.js: catch browser-launch failures inside the injected
  fetchAndExtractPriceViaBrowser wrapper so they route through
  checkProduct's normal error classification (recordCheckFailure)
  instead of escaping as a thrown error that bypasses the DB write.
- server.js: add an in-flight guard around runCheck so overlapping
  callers (cron + check-now) share one run instead of each launching
  its own Chromium.
- Dockerfile: copy only package.json/package-lock.json/node_modules
  before installing Chromium so the expensive install layer is keyed
  to dependency changes, not every commit; copy the rest of the app
  afterward.
- Dockerfile: clean up apt package lists after the Playwright install
  step, matching the build stage's existing cleanup.
- README.md: note that exercising the fallback locally (not just
  running the test suite) needs `npx playwright install chromium`.
- README.md: correct the fallback description — domcontentloaded
  navigation reads the page before most client-side JS finishes, so
  the fallback mainly helps with HTTP-client blocking, not JS-rendered
  prices; reworded to drop the inaccurate claim.

Co-Authored-By: Claude Sonnet 5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_013gwc3aCiyQxmCWQke8RvEz

Dockerfile

@@ -8,8 +8,11 @@ COPY . .
 
 FROM node:22-slim
 WORKDIR /app
+COPY --from=build /app/package.json /app/package-lock.json ./
+COPY --from=build /app/node_modules ./node_modules
+RUN npx --yes playwright install --with-deps chromium \
+    && rm -rf /var/lib/apt/lists/*
 COPY --from=build /app .
-RUN npx --yes playwright install --with-deps chromium
 ENV NODE_ENV=production
 # De SQLite-database hoort op het persistente volume te staan; zonder deze
 # default zou een vergeten DB_PATH stilletjes naar de container-fs schrijven