Example to demonstrate how to update field config in update hooks.

module.install

<?php

/**
 * @file
 * Contains install, update, uninstall hooks for module.
 */

use Drupal\field\Entity\FieldConfig;

/**
 * Implements hook_update_N().
 *
 * Enable translation for field_x field in vocabulary.
 */
function module_update_8001() {
  $config = \Drupal::configFactory()->getEditable('field.field.taxonomy_term.vocabulary.field_x');
  $config->set('translatable', TRUE);
  $config->save();

  $field = FieldConfig::loadByName('taxonomy_term', 'vocabulary', 'field_x');
  $field->setTranslatable(TRUE);
  $field->save();
}

We need to ensure FieldStorageConfig is also translatable.

`
foreach ($fields as $field) {
$fieldDefinition = $entityDefinitionUpdateManager->getFieldStorageDefinition($field, 'node');
if ($fieldDefinition && !$fieldDefinition->isTranslatable()) {
$fieldDefinition->setTranslatable(TRUE);
$entityDefinitionUpdateManager->updateFieldStorageDefinition($fieldDefinition);
}

$fieldStorageConfig = FieldStorageConfig::loadByName('node', $field);
if ($fieldStorageConfig) {
  $fieldStorageConfig->setTranslatable(TRUE);
  $fieldStorageConfig->save();
}

$fieldConfig = FieldConfig::loadByName('node', 'provider', $field);
if ($fieldConfig) {
  $fieldConfig->setTranslatable(TRUE);
  $fieldConfig->save();
}

}
`

Yep, thanks @purushotamrai