Add handling for large pipeline timeouts

What does this MR do?

Adds handling for cases in which large pipelines cause the GraphQL query to time out. See #323213 (closed) for more details and for a more graceful future fix.

Screenshots (strongly suggested)

See #323213 (closed).

Does this MR meet the acceptance criteria?

Conformity

• 📋 Does this MR need a changelog?
  • I have included a changelog entry.
  • I have not included a changelog entry because feature flag.
• Code review guidelines
• Merge request performance guidelines
• Style guides

Availability and Testing

• Review and add/update tests for this feature/bug. Consider all test levels. See the Test Planning Process.
• Tested in all supported browsers

Related to #276949 (closed)