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feat(docs): centralize code examples with dynamic variant tabs
This PR introduces a system for managing code examples centrally while
supporting file-based variant tabs (like html/script) within a single
code block.
## Changes
- **Extended variant system**: `PlatformCodeblock` now supports custom
variant names beyond just 'server'/'client', enabling tabs for any file
grouping (e.g., html/script pairs)
- **Vite example migration**: Moved vite-example.mdx code to
`code-examples/vite-example.ts` with html/script variants
- **LLM copy support**: The "Copy Markdown" button now expands
`PlatformCodeblock` components to inline the actual code, so LLMs
receive the full code examples instead of component references
## How it works
Code examples with variants are now displayed with filename-based tabs:
- Define examples with `variant: 'html'` and `variant: 'script'` in
`code-examples/`
- The tab labels automatically use the `filename` property
- When copying markdown for LLMs, all variants are included with their
filenames
<!-- This is an auto-generated comment: release notes by coderabbit.ai
-->
## Summary by CodeRabbit
## Release Notes
* **Documentation**
* Added a Vite JavaScript example guide with grouped auth examples
(init, index, password, OTP, OAuth) and wired examples into the
getting-started navigation.
* Removed the previous multi-page example guide and replaced it with the
new Vite-focused page.
* Documentation generation now expands platform code blocks to inline
concrete examples for clearer rendered docs.
* **Refactor**
* Improved code-example variant handling to support flexible variant
names for better tabbed/code-sample organization.
<sub>✏️ Tip: You can customize this high-level summary in your review
settings.</sub>
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