How will I access inner fields values in twig template
Similar question for the node id from today Reason for adding .value to access node id?

Either add .value to the field name

{{ author_picture['#user'].name.value }}


or use a specific method if the entity provides one:

{{ author_picture['#user'].getdisplayname }}


It is preferable to use  User:getDisplayName because it does extra processing:


  By default, the passed-in object's 'name' property is used if it
  exists, or else, the site-defined value for the 'anonymous' variable.
  However, a module may override this by implementing
  hook_user_format_name_alter(&amp;$name, $account).
  
  Return value
  
  string|\Drupal\Component\Render\MarkupInterface Either a string that
  will be auto-escaped on output or a MarkupInterface object that is
  already HTML escaped. Either is safe to be printed within HTML
  fragments.