e2e: Add GitHub Actions caching for dotcms-ui-e2e Playwright test suite

Description

The E2E test suite introduced in PR #33266 (feat(dotcms-ui-e2e): Make run E2E inside Nx) currently downloads Playwright browser binaries and node_modules on every CI run. Adding GitHub Actions caching for these artifacts will reduce E2E job startup time and lower overall PR pipeline duration.

The main caching targets are:

• ~/.cache/ms-playwright — Playwright browser binaries (~200–400MB download per run without cache)
• core-web/node_modules — yarn dependencies, if not already covered by existing Nx build workflow caching steps

Acceptance Criteria

• Playwright browser binaries are cached using actions/cache keyed on OS + core-web/package.json hash
• Cache invalidates correctly when the Playwright version changes (i.e. package.json update)
• node_modules cache is added if not already covered by existing Nx build caching steps
• Cache hit/miss is visible in CI run logs
• E2E pipeline startup time is measurably reduced on a cache hit run

Implementation Pattern

The expected caching pattern for the E2E job step in the relevant workflow file:

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

- name: Install Playwright browsers
  if: steps.playwright-cache.outputs.cache-hit \!= 'true'
  run: npx playwright install --with-deps chromium
  working-directory: core-web

The cache-hit conditional on the install step ensures browser binaries are only downloaded when the cache is cold or invalidated. The cache key uses package.json rather than yarn.lock because Playwright's binary version is declared in package.json directly — a lockfile change that doesn't update the Playwright version should still get a cache hit.

For node_modules, check whether the existing Nx build job steps already cache core-web/node_modules. If they do, reuse the same cache key in the E2E job rather than adding a duplicate step:

- name: Cache node_modules
  uses: actions/cache@v4
  with:
    path: core-web/node_modules
    key: node-modules-${{ runner.os }}-${{ hashFiles('core-web/yarn.lock') }}
    restore-keys: |
      node-modules-${{ runner.os }}-

Priority

Medium

Additional Context

This is Phase 1.1 of the agreed E2E testing rollout plan:

• Phase 1: Run E2E on every PR (current — PR #33266)
• Phase 1.1: Add GHA caching (this issue)
• Phase 2: Move to nightly when suite size warrants it
• Phase 3: On-demand trigger via PR label or manual workflow dispatch

Related: https://github.com/dotCMS/core/pull/33266

Locate the workflow containing the dotcms-ui-e2e job and compare its setup with the existing Nx build workflow, especially caching for core-web/node_modules. Add the Playwright cache and reuse any applicable dependency cache, then verify cache hit and miss behavior, browser installation, and reduced startup time in CI logs.