How to use setConstraints() for a custom constraint on BaseFieldDefinition?

Question

I'm refactoring a node content type into a custom entity.

On this entity, I add a datetime field:

$fields['target_date'] = BaseFieldDefinition::create('datetime')
          ->setLabel(t('Target date'))
          ->setCardinality(1)
          ->setRequired(TRUE)
          ->setConstraints(['DateTimeMidnightOnly' => DateTimeMidnightOnlyValidator::class])
          ->setSetting('datetime_type', 'datetime')
          ->setDisplayConfigurable('form', TRUE)
          ->setDisplayOptions('form', [
            'weight' => 10,
          ])
          ->setDisplayConfigurable('view', TRUE);

However, when I attempt to save a new entity of this entity type, I'm getting the following error:

Drupal\Core\Entity\EntityStorageException: No default option is configured for constraint "Drupal\mymodule\Plugin\Validation\Constraint\DateTimeMidnightOnly". in Drupal\Core\Entity\Sql\SqlContentEntityStorage->save() (line 811 of /app/web/core/lib/Drupal/Core/Entity/Sql/SqlContentEntityStorage.php).

I also tried this:

          ->setConstraints(['DateTimeMidnightOnly'])

Which gives the error:

Drupal\Core\Entity\EntityStorageException: The "0" plugin does not exist. Valid plugin IDs for Drupal\Core\Validation\ConstraintManager are: Callback, Blank, NotBlank, Email, CKEditor5Element, CKEditor5ToolbarItemDependencyConstraint, StyleSensibleElement, CKEditor5MediaAndFilterSettingsInSync, SourceEditingRedundantTags, CKEditor5EnabledConfigurablePlugins, CKEditor5FundamentalCompatibility, SourceEditingPreventSelfXssConstraint, UniqueLabelInList, CKEditor5ToolbarItemConditionsMet, CKEditor5ToolbarItem, CommentName, DateTimeFormat, ValidDynamicReference, FileValidation....

I'm clearly calling setConstraints() wrong, because this constraint worked when I added it on my content type using hook_entity_bundle_field_info_alter():

function mymodule_entity_bundle_field_info_alter(array &$fields, EntityTypeInterface $entity_type, string $bundle): void {
  $entity_type = $entity_type->id();
  if ($entity_type === 'node') {
    if (isset($fields['field_datetime_review_target'])) {
      $fields['field_datetime_review_target']->addConstraint('DateTimeMidnightOnly');
    }
  }
}

What's the right way to set ->setConstraints() to add a custom constraint plugin? Or, is this actually the wrong way and I should always use hook_entity_bundle_field_info_alter()?