Update Playwright Check Suite examples

[stefanjudis]

This is not ready to merge because I'm waiting for finalized URLs. I'm very keen on feedback though. :)

[Copilot]

Pull Request Overview

This PR refactors the repository to provide comprehensive examples of Playwright Check Suite configurations. It removes the old test files and replaces them with structured examples showing different use cases for synthetic monitoring with Checkly.

• Removes existing test files and creates organized example directories
• Updates configuration to demonstrate multiple Playwright Check Suite patterns
• Enhances documentation with detailed examples and best practices

Reviewed Changes

Copilot reviewed 14 out of 15 changed files in this pull request and generated 4 comments.

Show a summary per file

File	Description
tests/traces.spec.ts	Removed old trace testing example
tests/test-sessions.spec.ts	Removed old test session example
tests/please.cleanup.ts	Removed cleanup demonstration file
tests/login.setup.ts	Removed old authentication setup
tests/homepage.spec.ts	Removed old homepage test
tests/home-dashboard.spec.ts	Removed old dashboard test
tests/example-4/login.setup.ts	Added new authentication setup example
tests/example-4/homepage.spec.ts	Added logged-in test example
tests/example-3/homepage.spec.ts	Added tagged test example
tests/example-2/homepage.spec.ts	Added environment-specific test example
tests/example-1/homepage.spec.ts	Added basic multi-browser test example
playwright.config.ts	Restructured to demonstrate four different configuration patterns
checkly.config.ts	Updated with detailed examples and comprehensive documentation
README.md	Complete rewrite with detailed examples and usage instructions

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