How to create suggestions conditionally (by block type/bundle) override system templates in Drupal 8
Currently, I have only found a workaround using image-formatter override

Create a file name suggestion hook for theme in themename.theme:

function themename_theme_suggestions_alter(array &amp;$suggestions, array $variables, $hook) {
    switch ($hook) {
        case 'image_formatter':

            /**
             * @var Drupal\url_image\Plugin\Field\FieldType\UrlImageItem $item
             */
            $item = $variables['item'];
            $config = $item-&gt;getFieldDefinition();
            switch ($config-&gt;getTargetBundle()) {
                case 'b_partner_images':
                    $suggestions[] = 'image_formatter__b_partner_images';
                    break;
            }
            break;
    }
}


Create a template file image-formatter--b-partner-images.html.twig:

&lt;a href="{{ url }}" title="{{ image['#alt'] }}" target="_blank"&gt;
     &lt;div class="image" style="background-image: url('{{ file_url(image['#uri']) }}');"&gt;&lt;/div&gt;
&lt;/a&gt;


It works, but not as beautifully, as I would like.

PS: I used that specific hook_theme_suggestions_alter format, because I have more than one suggestions hook, and I put them inside this single function, so I can add more conditions with ease.