I encountered this issue when upgrading from Drupal 8 to  

Mismatched entity and/or field definitions The following changes were detected in the entity type and field definitions. Paragraph The paragraph.field_background_fixed field needs to be updated.

Since <drush entup> is deprecated you would need to install the Devel Entity Updates for this. How I fixed this was to write a simple hook_update() function in my custom module:

/**
 * Drupal 9 upgrade: "Mismatched entity and/or field definition” when “drush entity-updates” fails?"
 */
function mymodule_update_9020() {
  $manager = \Drupal::entityDefinitionUpdateManager();
  if ($field = $manager->getFieldStorageDefinition('field_background_fixed', 'paragraph')) {
    $manager->updateFieldStorageDefinition($field);
  }
}

After the update, the error disappeared!