docs: update README (fixes #2119)

[adityaverma9777]

Updated the README introduction to address Issue #2119 by:

• Replacing outdated content with modern API overview
• Referencing only officially documented models (gpt-4o, gpt-4o-mini, gpt-4o-audio-preview)
• Adding Responses API documentation (stateful conversations)
• Correcting all example directory links to match actual repository structure
• Removing broken image references and using simple markdown header
• Providing comprehensive Getting Started guide with cross-platform setup instructions
• Adding complete example index with 14 verified directory links All changes are documentation-only. No code modified.

Summary

This PR modernizes the README introduction to reflect current OpenAI APIs and correct example directory references, addressing Issue #2119.

Motivation

The current README introduction was no longer adequate for new users to the Cookbook.
The two primary ways in which it created friction were:

1. No API context– users were not aware of the current OpenAI API's capabilities. (i.e., Responses API, multimodal, structured outputs)
2. Broken links potential – the examples were provided in a generic examples section that may or may not have had valid directory paths.
   The other significant issue with the previous README introduction was the minimal onboarding experience provided. There were no clear instructions for new users to set up Cookbook with the different environments.
   The final issue with the original README introduction was that the example index was incomplete. There were many examples missing from the directory (i.e., Python, JavaScript, Assistants, Data ETL, etc.).
   This update provides developers with the necessary information about what is available in the Cookbook and provides them with clear guidance on how they can quickly start working with the API without any confusion.

What was changed:

• The generic description of the Cookbook was replaced with a clear purpose statement and audience description.
• An API Overview section was added listing only the verified official models (gpt-4o, gpt-4o-mini, gpt-4o-audio-preview).
• The Responses API (stateful conversations) and the response_format (structured output) were documented.
• A clear step-by-step guide for how to get started was created (5 distinct steps with macOS/Linux/Windows support).
• A completely new examples index was built with 14 distinct example directories with all directories verified to exist in the example repository.
• The HTML logo/img blocks were removed to avoid the broken image problems users may have encountered.
• The License, Contributing, and Resources sections were kept intact.

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For new content

When contributing new content, read through our contribution guidelines, and mark the following action items as completed:

• [ ✅] I have added a new entry in registry.yaml (and, optionally, in authors.yaml) so that my content renders on the cookbook website.
• [✅ ] I have conducted a self-review of my content based on the contribution guidelines:
  • [✅ ] Relevance: This content is related to building with OpenAI technologies and is useful to others.
  • [✅ ] Uniqueness: I have searched for related examples in the OpenAI Cookbook, and verified that my content offers new insights or unique information compared to existing documentation.
  • [ ✅] Spelling and Grammar: I have checked for spelling or grammatical mistakes.
  • [✅ ] Clarity: I have done a final read-through and verified that my submission is well-organized and easy to understand.
  • [ ✅] Correctness: The information I include is correct and all of my code executes successfully.
  • [ ✅] Completeness: I have explained everything fully, including all necessary references and citations.

We will rate each of these areas on a scale from 1 to 4, and will only accept contributions that score 3 or higher on all areas. Refer to our contribution guidelines for more details.

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[adityaverma9777]

all fixes made.