Update existing BaseField definition size

If you want to update the base field size then you can do by using some hooks. Use hook_entity_base_field_info_alter to increase the size in the form

<?php
use Drupal\Core\Entity\EntityTypeInterface;
/**
 * Implements hook_entity_base_field_info_alter().
 */
function burndown_extend_entity_base_field_info_alter(&$fields, EntityTypeInterface $entity_type) {
  /** @var \Drupal\Core\Field\BaseFieldDefinition $fields[] */
  if ($entity_type->id() === 'burndown_task') {
    $fields['name']->setSetting('max_length', 255);
  }
}

Once you implement the above then still you need to update the field storage etc in the database. You can use the hook_update_n to update the storage

<?php

/**
 * Implements hook_update_N().
 *
 * Update the task name field size.
 */
function burndown_extend_update_8001(&$sandbox) {
  burndown_extend_db_change_varchar_field('burndown_task', 'name', 255);
}


/**
 * Change length of a varchar entity field with data, safe with entity-updates.
 *
 * This updates the storage schema, the database schema, and the last
 * installed schema.
 *
 * The entity schema must also be changed in code in the entities
 * baseFieldDefinitions() or in an alter.
 *
 * @param string $entity_type_id
 *   The entity type.
 * @param string $field_name
 *   The field name to change.
 * @param int $field_length
 *   The new length of the field, must be larger than the previous value.
 */
function burndown_extend_db_change_varchar_field($entity_type_id, $field_name, $field_length) {
  /** @var \Drupal\Core\Entity\EntityLastInstalledSchemaRepositoryInterface $schema_repository */
  $schema_repository = \Drupal::service('entity.last_installed_schema.repository');
  /** @var \Drupal\Core\Entity\EntityFieldManager $entity_field_manager */
  $entity_field_manager = \Drupal::service('entity_field.manager');
  $base_field_definitions = $entity_field_manager->getBaseFieldDefinitions($entity_type_id);
  $schema_repository->setLastInstalledFieldStorageDefinition($base_field_definitions[$field_name]);
  $field_storage_definitions = $schema_repository->getLastInstalledFieldStorageDefinitions($entity_type_id);

  // Update the field definition in the last installed schema repository.
  $schema_repository->setLastInstalledFieldStorageDefinitions($entity_type_id, $field_storage_definitions);

  // Update the storage schema.
  $key_value = \Drupal::keyValue('entity.storage_schema.sql');
  $key_name = $entity_type_id . '.field_schema_data.' . $field_name;
  $storage_schema = $key_value->get($key_name);
  // Update all tables where the field is present.
  foreach ($storage_schema as &$table_schema) {
    $table_schema['fields'][$field_name]['length'] = $field_length;
  }
  $key_value->set($key_name, $storage_schema);

  // Update the database tables where the field is part of.
  $db = Drupal::database();
  foreach ($storage_schema as $table_name => $table_schema) {
    $db->schema()->changeField($table_name, $field_name, $field_name, $table_schema['fields'][$field_name]);
  }
}