chore: Run browser contract tests in CI.

[kinyoklion]

This PR adds support for running the browser contract tests in CI. The browser contract tests need to run in a browser to ensure test efficacy and this is accomplished using playwright in CI.

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Note

Adds CI steps to build, serve, and run browser contract tests via Playwright, plus supporting scripts/docs and Playwright dependency.

• CI / GitHub Actions (.github/workflows/browser.yml):
  • Build and run browser contract tests: install Playwright browsers, build browser-contract-test-adapter and browser-contract-test-service, start adapter/WebSocket and static server, wait for readiness, open headless Chromium, run contract tests via launchdarkly/contract-tests action, and add failure logs/cleanup.
• Contract Tests (packages/sdk/browser/contract-tests/):
  • Docs: Add README.md describing architecture and local run instructions.
  • Entity service:
    • Add open-browser.mjs to launch headless Chromium and stream console/errors.
    • Update entity/package.json: add playwright devDependency and install-playwright-browsers script.

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[github-actions]

@launchdarkly/browser size report
This is the brotli compressed size of the ESM build.
Compressed size: 169118 bytes
Compressed size limit: 200000
Uncompressed size: 789399 bytes

[github-actions]

@launchdarkly/js-sdk-common size report
This is the brotli compressed size of the ESM build.
Compressed size: 24988 bytes
Compressed size limit: 26000
Uncompressed size: 122411 bytes

[github-actions]

@launchdarkly/js-client-sdk-common size report
This is the brotli compressed size of the ESM build.
Compressed size: 17636 bytes
Compressed size limit: 20000
Uncompressed size: 90259 bytes

[github-actions]

@launchdarkly/js-client-sdk size report
This is the brotli compressed size of the ESM build.
Compressed size: 21981 bytes
Compressed size limit: 25000
Uncompressed size: 75580 bytes