[Docs] Reorganize examples docs.

[noooop]

Purpose

Following #29362

Reorganize examples docs.

Test Plan

Test Result

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Essential Elements of an Effective PR Description Checklist

• The purpose of the PR, such as "Fix some issue (link existing issues this PR will resolve)".
• The test plan, such as providing test command.
• The test results, such as pasting the results comparison before and after, or e2e results
• (Optional) The necessary documentation update, such as updating supported_models.md and examples for a new model.

[mergify]

Documentation preview: https://vllm--41082.org.readthedocs.build/en/41082/

[gemini-code-assist]

Code Review

This pull request removes the categorized list of example links from the main examples README, leaving the document essentially empty. Feedback indicates that this change significantly hinders discoverability and suggests that any reorganization should maintain navigation links to ensure the documentation remains useful.

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docs/examples/README.md (3-7)

Removing the list of example categories makes it very difficult for users to discover the available examples. This change leaves the main examples page almost empty, which can be confusing.

If the intention is to move this index to another location as part of the reorganization, that change should be included in this pull request to ensure the documentation remains navigable.

[claude]

Claude Code Review

This pull request is from a fork — automated review is disabled. A repository maintainer can comment @claude review to run a one-time review.