Tags not working in my custom post type

by

“Tags” are a taxonomy and should be registered using the taxonomy argument, not the supports argument.

taxonomies (array) (optional) An array of registered taxonomies like category or post_tag that will be used with this post
type. This
can be used in lieu of calling register_taxonomy_for_object_type()
directly. Custom taxonomies still need to be registered with
register_taxonomy().
Default: no taxonomies

https://codex.wordpress.org/Function_Reference/register_post_type#Arguments