Currently, the Input component's type is hardcoded to "text" (line 816):
https://github.com/pacocoursey/cmdk/blob/d6fde235386414196bf80d9b9fa91e2cf89a72ea/cmdk/src/index.tsx#L802-L825

This means we can't set it to "search" in order to support browsers' built-in clear functionality/user agent styling.