Make tests cache-independent by clearing cache before and after

What does this MR do and why?

This MR does two things:

• Always clear cache before and after examples
• Disallow any real HTTP requests

Expected impact & dry-runs

More stable test suite.

Action items

• If adding environment variables for reactive processors, update config/triage-web.yaml and .gitlab/ci/triage-web.yml
• (If applicable) Add documentation to the handbook pages for Triage Operations =>
• (If applicable) Identify the affected groups and how to communicate to them:
  • /cc @person_or_group =>
  • Relevant Slack channels =>
  • Engineering week-in-review