[codex] Rewrite how to work with large language models

[paytonison]

Summary

• Rewrite articles/how_to_work_with_large_language_models.md into a current first-time user guide for working with LLMs.
• Update examples and guidance around the Responses API, model choice, prompting, structured outputs, retrieval, tool use, conversation state, evals, safety, optimization, and fine-tuning.
• Add paytonison to authors.yaml and update the article metadata in registry.yaml.

Motivation

The existing article was centered on older GPT-3/GPT-4 and legacy completions-era guidance. This refresh makes the article more useful for new users and aligns it with current OpenAI API concepts.

Validation

• git diff --check HEAD~1..HEAD
• Parsed authors.yaml and registry.yaml with Python/YAML
• Checked Markdown reference links for missing or unused definitions