refactor: refactor request and response example

[dsuket]

Description

Since there were many shared parts between createRequestExample and createResponseExample, I refactored and cleaned them up.

Motivation and Context

To address Issue #1158, I need to organize the example-related parts.
This is the first step toward that goal.

How Has This Been Tested?

• Pass npm run build
• Pass npm run test
• I went through the demo API and tests and confirmed that the examples are being displayed properly.

Screenshots (if appropriate)

Types of changes

• Bug fix (non-breaking change which fixes an issue)
  • Refactoring

Checklist

• I have updated the documentation accordingly.
• I have read the CONTRIBUTING document.
• I have added tests to cover my changes if appropriate.
• All new and existing tests passed.

[github-actions]

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