<?php
  $file_uri = $user->get('user_picture')->entity->getFileUri();
  dpm($file_uri); //correct uri
  $styled_image_url = ImageStyle::load("user_pic")->buildUrl($file_uri);
  dpm($styled_image_url); //correct url
  $picture = $styled_image_url;
  $variables['user_pic'] = $picture;

<div class="user-info right-menu" nav-id="{{attributes.id}}">
  <img src="{{ user_pic }}">
</div>