What is wp_get_post_tags for media tags?

If I understand correctly, wp_get_post_tags returns the “post_tags”
taxonomy terms.

Yes, except that the taxonomy is post_tag and not post_tags.

How can I access “attachment_keywords” taxonomy terms?

wp_get_post_tags() uses wp_get_post_terms(), so you would do the same for custom taxonomies.

For example if the taxonomy (name/slug) is attachment_keywords, then:

$tags = wp_get_post_terms( $post->ID, 'attachment_keywords' );

And that should work, but as suggested in the documentation for wp_get_object_terms() that’s used by wp_get_post_terms(), you might want to use get_the_terms() instead which caches the results and thus can help improve performance, specifically when looping over posts results.