Add Datadog Synthetic tests workflow

[Copilot]

Integrates Datadog Synthetic tests into CI/CD pipeline via GitHub Actions.

Changes

• New workflow .github/workflows/datadog-synthetic.yml
  • Triggers on push/PR to trunk
  • Authenticates via DATADOG_API_KEY and DATADOG_APP_KEY secrets
  • Uses DataDog/synthetics-ci-github-action@v1

Required Setup

Repository secrets must be configured:

• DATADOG_API_KEY
• DATADOG_APP_KEY

- name: Run Datadog Synthetic tests
  uses: DataDog/synthetics-ci-github-action@v1
  with:
    api_key: ${{ secrets.DATADOG_API_KEY }}
    app_key: ${{ secrets.DATADOG_APP_KEY }}

Original prompt

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This section details on the original issue you should resolve

<issue_title>## Pull request overview</issue_title>
<issue_description>## Pull request overview

This pull request adds a GitHub Actions workflow for integrating Datadog Synthetic tests into the CI/CD pipeline. The workflow triggers automated end-to-end tests when code is pushed or pull requests are opened against the main branch.

Changes:

• Added new GitHub Actions workflow configuration for Datadog Synthetic test integration
• Configured workflow to trigger on push and pull request events to the main branch
• Set up Datadog API and Application key authentication via GitHub secrets

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Originally posted by @copilot-pull-request-reviewer in microsoft/vscode-livepreview#772 (review)</issue_description>

Comments on the Issue (you are @copilot in this section)

• Fixes ## Pull request overview #4

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