I want to separate the processing of public sites by administrator privileges

While logged in to the WordPress administration screen with administrator privileges, I would like to separate the items to be displayed from regular users when I open a public site.

The public site tried to retrieve user information using wp_get_current_user, but failed to retrieve the user information.
While logged in to the administration screen, I am browsing with the same browser, but the public site cannot retrieve it.

When I dump it on the management screen, the user information appears, but will it not be handed over to the public site?

Also, if you know how to determine if you are an administrator and sort out the process, I would appreciate it if you could let me know.

My theme is storefront.
https://ja.wordpress.org/themes/storefront/

wp_get_current_user()

object(WP_User)#9332(8){
  ["data"] =>
  object(stdClass)#9345(0){
  }
  "ID" = >
  int(0)
  ["caps"] = >
  array(0){
  }
  ["cap_key"] =>
  Null
  "roles" = >
  array(0){
  }
  "allcaps" = >
  array(0){
  }
  ["filter"] =>
  Null
  ["site_id":"WP_User":private] =>
  int(0)
}