[docs] Improve custom error logging callback example

[AryanSharma48]

Problem

SmoothAPI supports callbacks for handling non-retryable errors, but the
current documentation provides only a very basic example.

A more realistic example would help users understand how the callback can
be used in an application.

What needs to be done

Improve the relevant TypeScript README documentation by adding a
realistic example of handling and logging a non-retryable error.

The example should demonstrate how an application could:

• Receive the error
• Extract useful information
• Log or report the error
• Continue with the application's error-handling flow

Acceptance Criteria

• A realistic callback example is included
• The example uses the current SmoothAPI API
• The example is valid TypeScript
• The callback behavior is clearly explained
• Existing documentation remains accurate

Files to look at

• packages/smooth-api-ts/README.md

Prerequisites

Basic TypeScript and Markdown.

Notes

The example does not need to integrate an actual external logging service.
A realistic illustrative example is sufficient.