docs: add TokenLab OpenAI-compatible instrumentation example

[hedging8563]

Summary

• Show OpenLLMetry's OpenAI instrumentation with a TokenLab base_url.
• Keep the change docs-only and scoped to the project's existing OpenAI-compatible configuration surface.

Validation

• git diff --check

Summary by CodeRabbit

• Documentation
  • Expanded the example usage guide with an additional Python example.
  • Clarified that instrumentation works with OpenAI-compatible base_url configurations.
  • Added a sample showing how to create a client with a custom endpoint and trace chat completion requests.

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Supersedes #4354. The previous PR was closed while fixing contributor commit metadata; this replacement branch preserves the same scoped diff with commits authored by hedging8563 <45883076+hedging8563@users.noreply.github.com>.

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All committers have signed the CLA.

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No actionable comments were generated in the recent review. 🎉

ℹ️ Recent review info

⚙️ Run configuration

Configuration used: defaults

Review profile: CHILL

Plan: Pro

Run ID: a5270e97-b38a-4d55-8b83-1919a8032aac

📥 Commits

Reviewing files that changed from the base of the PR and between 93429cf and 20be7ee.

📒 Files selected for processing (1)

• packages/opentelemetry-instrumentation-openai/README.md

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📝 Walkthrough

Walkthrough

Updated the README for the OpenAI instrumentation package to add a documentation section and Python code example illustrating that the instrumentation works with the OpenAI SDK when configured with a custom base_url, such as for OpenAI-compatible endpoints.

Changes

README Documentation Update

Layer / File(s)	Summary
Add base_url usage example packages/opentelemetry-instrumentation-openai/README.md	Added a paragraph and Python code snippet to the Example usage section demonstrating instrumentation with an OpenAI-compatible endpoint via base_url configuration.

Estimated code review effort: 1 (Trivial) | ~2 minutes

🚥 Pre-merge checks | ✅ 5

✅ Passed checks (5 passed)

Check name	Status	Explanation
Description Check	✅ Passed	Check skipped - CodeRabbit’s high-level summary is enabled.
Title check	✅ Passed	The title accurately summarizes the docs-only addition of a TokenLab OpenAI-compatible instrumentation example.
Docstring Coverage	✅ Passed	No functions found in the changed files to evaluate docstring coverage. Skipping docstring coverage check.
Linked Issues check	✅ Passed	Check skipped because no linked issues were found for this pull request.
Out of Scope Changes check	✅ Passed	Check skipped because no linked issues were found for this pull request.

✨ Finishing Touches

🧪 Generate unit tests (beta)

• Create PR with unit tests

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[hedging8563]

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