Show post type taxonomy

Set the public parameter in register_post_type to true like this:

public'             => true,

public
(boolean) (optional) Controls how the type is visible to authors (show_in_nav_menus, show_ui) and readers (exclude_from_search, publicly_queryable).

Default: false

‘true’ – Implies exclude_from_search: false, publicly_queryable, show_in_nav_menus, and show_ui. The built-in types attachment, page, and post are similar to this.

And create a search.php file.