[META] Improve Elastic Inference documentation

## Summary

Users searching for **Elastic inference** currently land on fragmented or partial documentation that does not clearly explain core concepts or guide them through a complete workflow.

This META issue tracks the work required to create a cohesive, end-to-end documentation experience that helps users:
- understand what Elastic Inference is
- implement common use cases (semantic search, chat completion, reranking)
- optimize and troubleshoot their workflows

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## Goals

- Provide a clear entry point for Elastic Inference
- Cover the most important use cases end-to-end
- Connect conceptual docs, tutorials, and APIs into a guided journey
- Document the inference API as the replacement for deprecated AI connectors

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## Success criteria

- Users can go from **"What is Elastic Inference?" → "I built a working use case"** without leaving the docs ecosystem
- Core use cases (semantic search, chat completion, reranking) are fully documented end-to-end
- Clear navigation and linking between concepts, APIs, and tutorials
- Migration path from deprecated AI connectors is documented

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## Collaboration

This effort requires coordination between:
- Docs team
- Dev team
- SMEs (inference, AI Features for connector deprecation messaging)

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## Notes

- Replaces https://github.com/elastic/docs-content-internal/issues/119
- AI connectors (OpenAI, Bedrock, Gemini, Elastic Inference connectors) are deprecated as of stack 9.5 / serverless — elastic/docs-content-internal#1668 covers the migration path to the inference API
- Completed work: API documentation completeness review (#280), chunking section examples (#273)