Cleanup: Remove orphan docs pages and Docusaurus template files (#17356)

* docs: update getting started page

- Add Core Functions table with link to full list
- Add Responses API section
- Add Async section with acompletion() example
- Add "Switch Providers with One Line" example
- Clarify Basic Usage supports multiple endpoints
- Update models to current versions (openai/gpt-4o, anthropic/claude-sonnet-4)
- Use provider/model format throughout
- Fix deprecated import: from openai.error -> from openai
- Keep original structure: community key, More details links, observability env vars

* Cleanup: Remove orphan docs pages and Docusaurus template files

- Remove orphan getting_started.md (not linked in sidebar)
- Remove Docusaurus template intro.md
- Remove tutorial-basics/ directory (Docusaurus template)
- Remove tutorial-extras/ directory (Docusaurus template)

Author: Chesars