Cache Playwright browsers in CI

[gkorland]

Parent issue

Part of #550 (CI Pipeline Optimization Analysis)

Problem

The Playwright workflow installs browsers from scratch every run (npx playwright install --with-deps), taking ~50s per shard (~1.5 min total across 2 shards).

Solution

Add actions/cache for the Playwright browser binaries:

- name: Cache Playwright browsers
  id: playwright-cache
  uses: actions/cache@v4
  with:
    path: ~/.cache/ms-playwright
    key: playwright-${{ runner.os }}-${{ hashFiles('package-lock.json') }}

- name: Install Playwright Browsers
  if: steps.playwright-cache.outputs.cache-hit != 'true'
  run: npx playwright install --with-deps chromium

- name: Install Playwright system deps
  if: steps.playwright-cache.outputs.cache-hit == 'true'
  run: npx playwright install-deps chromium

Estimated savings

~1.5 min per CI run

Effort

Low