You are most probably using add_theme_support() in the wrong context (hook).
Because you are registering the post type yourself, all you need to do is to add support for thumbnails in the supports array when you pass your your arguments to register_post_type()
supports(array/boolean) (optional) An alias for calling
add_post_type_support()directly. As of 3.5, boolean false can be passed as value instead of an array to prevent default (title and editor) behavior.Default: title and editor
All you need to do is to pass thumbnail to the array
'supports' => ['title', 'editor', 'thumbnail'], // Add additional values as needed
You would also need to check if support for thumbnails is enabled by the theme, and if not, add post thumbnail support in your plugin.