How to get translated field_storage_config
How is this possible and how can I programmatically set the
  translations for my field(s)?


You can load language overrides with ConfigurableLanguageManager::getLanguageConfigOverride, set values and save:

\Drupal::languageManager()-&gt;getLanguageConfigOverride('fr', 'field.storage.node.field_example')
  -&gt;set($key, $value)
  -&gt;save();