[FEATURE] design-sync for react native

### Preflight Checklist

- [x] I have searched [existing requests](https://github.com/anthropics/claude-code/issues?q=is%3Aissue%20label%3Aenhancement) and this feature hasn't been requested yet
- [x] This is a single feature request (not multiple features)

### Problem Statement

It would be nice to also support react native or react native web

### Proposed Solution

add support for react native or react native web

### Alternative Solutions

_No response_

### Priority

Medium - Would be very helpful

### Feature Category

CLI commands and flags

### Use Case Example

Same use case as current design-sync for React

### Additional Context

_No response_

Start by reviewing the existing design-sync for React and the CLI commands and flags it uses. Determine the required behavior for React Native and React Native Web, including how support can be verified; done means the same design-sync use case works for the requested platforms.

Written by the indexing model from the issue text.