Reduce E2E CI flake from Playwright browser install

E2E staging job often timeout because CI downloads all Playwright browsers with deps, then waits fixed sleep 180. We could install only Chromium or use Playwright Docker image and replace fixed sleep with readiness check

Start by locating the E2E staging CI job and its Playwright browser installation and fixed 180-second sleep. Compare the issue's Chromium-only and Playwright Docker image options, then verify that a readiness check prevents the staging job from timing out and that the E2E job still runs successfully.

Written by the indexing model from the issue text.