Resolve "Using the Web IDE Web Terminal leads to error 500 when accessing the dashboard/projects list"

What does this MR do?

Adds a check around pipeline status caching so that only the CI pipeline statuses are cached. This means the WebIDE Terminal pipeline status will no longer be cached unnecessarily.

This is being done because caching of the terminal pipeline status causes a 500 error when trying to view the projects dashboard after starting a terminal pipeline (see #197130 (closed)).

The dashboard uses project.pipeline_status to determine if it should show a pipeline status icon. This method was returning a cached terminal pipeline status, which then caused the detailed_status error described in the related issue.

Does this MR meet the acceptance criteria?

Conformity

• Changelog entry
• Documentation (if required)
• Code review guidelines
• Merge request performance guidelines
• Style guides
• Database guides
• Separation of EE specific content

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
• Informed Infrastructure department of a default or new setting change, if applicable per definition of done

Security

If this MR contains changes to processing or storing of credentials or tokens, authorization and authentication methods and other items described in the security review guidelines:

• Label as security and @ mention @gitlab-com/gl-security/appsec
• The MR includes necessary changes to maintain consistency between UI, API, email, or other methods
• Security reports checked/validated by a reviewer from the AppSec team

Closes #197130 (closed)