feat: add response syntax highlighting to API playground

[rohilsurana]

Problem

The API playground dialog (`src/components/api/playground-dialog.tsx`) displays raw JSON responses without syntax highlighting. The response body tab shows plain monospace text, making it hard to read large responses.

Suggested Fix

• Use the existing Shiki setup or CodeMirror (already imported for the request body editor) to highlight the response JSON
• Apply the same dark/light theme as the rest of the site