SearchInput

Add the brand-ui SearchInput component (from @elabs-ai/components-data) to this project.

1. Read https://elabs-ai.com/llms.txt first: it maps every package and the rules. If you can use MCP servers, connect https://elabs-ai.com/mcp and use its search, docs and tokens tools. If not, run the same lookups in the terminal: `npx -y @elabs-ai/components-cli search "<what you need>"` and `npx -y @elabs-ai/components-cli docs <Component>`.
2. Look SearchInput up before writing code: `npx -y @elabs-ai/components-cli docs SearchInput` prints its real props, variants, what it pairs with and what to avoid.
3. If @elabs-ai/components-data is not installed yet: `pnpm add @elabs-ai/components-tokens @elabs-ai/components-ui @elabs-ai/components-data` (or `npm install @elabs-ai/components-tokens @elabs-ai/components-ui @elabs-ai/components-data`). If this is the first brand-ui package in the project, wire it once: import `@elabs-ai/components-tokens/styles.css` plus the `themes/light.css` and `themes/dark.css` stylesheets in the CSS entry, add one Tailwind `@source` line per installed @elabs-ai package (Tailwind does not scan node_modules, so without it everything renders unstyled), and wrap the app root in `ThemeProvider` from `@elabs-ai/components-tokens`.
4. Use it here: [the screen or file, and what it should show]
5. Rules: use only @elabs-ai/components-* components and the semantic tokens — no raw colours, no raw font sizes, no arbitrary Tailwind values. Look up each component's real props with the docs tool before you use it; never guess a prop.
6. Done means: the typecheck passes, `npx -y @elabs-ai/components-cli audit src --strict` reports nothing, and you have opened the app and looked at every screen you touched in the light and the dark theme.