Passing variables to custom block
For a custom template use your own theme hook etypeservices:

function etypeservices_theme($existing, $type, $theme, $path) {
   return [
    'etypeservices' =&gt; [
      'variables' =&gt; [
        'facebook' =&gt; '',
     ],
   ],
];
}


Which uses it's own variables space:

public function build() {
    $config = \Drupal::config('etypeservices.settings');
    $facebook = $config-&gt;get('facebook');
    return [
      '#theme' =&gt; 'etypeservices',
      '#facebook' =&gt; $facebook,
   ];
 }
}


etypeservices.html.twig

{{ facebook }}


The content of the block is a normal render array, which can contain one or more custom templates to make them accessible in theming. These custom templates are reusable, not only in blocks.

In a module you can override the block template, as you tried to do by using block__..., but you need this in very rare cases. In drupal core there is only one. Then you will inherit the variables of the base hook block. 

But normally you leave the block template as it is, so that it can be themed on it's own.