How to show notice alert only on product dashboard page?

If you’re on wp-admin/post.php, you’ve got either

• global $post_type
• or possibly $_POST['post_type'], if we don’t have a post ID to look up the type from

that you can test for ‘product’. See the first 50 lines of wp-admin/post.php.

As an aside, I don’t think you need to check for is_admin in a admin_init handler; nor do you need to check if your plugin is enabled if this code is in the same plugin, since it won’t be run unless the plugin is enabled. Unless you’re testing for a different plugin that is.