How to update a field storage length in hook_install (or hook_update). Note this does not cover more difficult things, like changing storage type altogether.

mymodule.php

<?php

use Drupal\Core\Database\Database;

/**
 * Implements hook_install().
 */
function mymodule_install() {
  $connection = Database::getConnection('default');

  // Modify tables directly. field.storage.paragraph.field_question
  drupal_set_message('paragraph__field_question: altering database tables.', 'warning');
  $connection->query(
    'ALTER TABLE paragraph_revision__field_question MODIFY field_question_value varchar(512);'
  );
  $connection->query(
    'ALTER TABLE paragraph__field_question MODIFY field_question_value varchar(512);'
  );

  // Force configuration to be set to match.
  drupal_set_message('Checking config for any required updates.');
  $config_factory = \Drupal::configFactory();
  $config = $config_factory->getEditable('field.storage.paragraph.field_question');
  if ($config->get('settings.max_length') != 512) {
    drupal_set_message('Config needs updating; updating.', 'warning');
    $config->set('settings.max_length', 512);
    $config->save();
  }
  else {
    drupal_set_message('Config has already been updated.');
  }

  // Live schemas.
  drupal_set_message('Checking live schema matches database.');
  $store = \Drupal::service("keyvalue")->get("entity.storage_schema.sql");
  $data = $store->get("paragraph.field_schema_data.field_question");
  $live_schema_change = FALSE;
  foreach (["paragraph_revision__field_question", "paragraph__field_question"] as $table) {
    if ($data[$table]["fields"]["field_question_value"]["length"] != 512) {
      $data[$table]["fields"]["field_question_value"]["length"] = 512;
      $live_schema_change = TRUE;
    }
  }
  if ($live_schema_change) {
    drupal_set_message('Live schema needs updating; updating.', 'warning');
    $store->set("paragraph.field_schema_data.field_question", $data);
  }
  else {
    drupal_set_message('Live schema has already been updated.');
  }

  // Last-installed schemas.
  $schema_repository = \Drupal::service("entity.last_installed_schema.repository");
  $last_max_length = $schema_repository->getLastInstalledFieldStorageDefinitions("paragraph");
  $last_max_length = $last_max_length["field_question"]->getSetting("max_length");

  if ($last_max_length != 512) {
    drupal_set_message('Last installed schema record needs updating; updating.', 'warning');
    $field_storage_definitions = \Drupal::entityManager()->getFieldStorageDefinitions("paragraph");
    $field_storage_definitions["field_question"]->setSetting("max_length", 512);
    // Now set as the most recent schema definition.
    $schema_repository->setLastInstalledFieldStorageDefinitions(
      "paragraph", $field_storage_definitions
    );
  }
  else {
    drupal_set_message('Last installed schema record has already been updated.');
  }
}