How can I extend Serializer to handle a custom field type?

I'm trying to extend Serialization to get the JSON Field module to return a JSON object instead of stringified JSON.

Goal: When I access an entity that contains a JSON field using JSON:API, I want a JSON object for the field value (currently, the stringified JSON is returned).

I think what I need to do is to extend one of the core normalizers and use it to add a json_decode() step.

There is some documentation on how Serializer handles entities but it is out-of-date (last updated in 2017 before JSON:API was part of core, and the current code looks nothing like what is shown.)

I tried extending FieldNormalizer in /json_field/src/Normalizer/JsonFieldNormalizer.php.
However, I'm not confident that this is the correct approach, as there is also a FieldItemNormalizer and TypedDataNormalizer. To change how a field is output in JSON:API, which class should I extend?

<?php

namespace Drupal\json_field\Normalizer;

use Drupal\Core\Field\FieldDefinitionInterface;
use Drupal\json_field\Plugin\Field\FieldType\NativeJSONItem;
use Drupal\jsonapi\JsonApiResource\ResourceObject;
use Drupal\jsonapi\Normalizer\FieldNormalizer;
use Drupal\jsonapi\Normalizer\Value\CacheableNormalization;
use Drupal\jsonapi\ResourceType\ResourceType;

class JsonFieldNormalizer extends FieldNormalizer {

  /**
   * {@inheritdoc}
   */
  protected $supportedInterfaceOrClass = NativeJSONItem::class;

  /**
   * {@inheritdoc}
   */
  public function normalize($field, $format = NULL, array $context = []) {
    $field_name = $field->getName();
    \Drupal::logger('json_field')->info("Field has name $field_name");
    assert($field instanceof NativeJSONItem);
    /** @var \Drupal\Core\Field\FieldItemListInterface $field */ $normalized_items = $this->normalizeFieldItems($field, $format, $context);
    assert($context['resource_object'] instanceof ResourceObject);
    return $context['resource_object']->getResourceType()->getFieldByInternalName($field->getName())->hasOne()
      ? array_shift($normalized_items) ?: CacheableNormalization::permanent(NULL)
      : CacheableNormalization::aggregate($normalized_items);
  }

And I added the class to json_field.services.yml:

services:
  json_field.views:
    class: Drupal\json_field\JSONViews
  json_field.normalizer.field.json_field:
    class: Drupal\json_field\Normalizer\JsonFieldNormalizer
    tags:
      - { name: normalizer, priority: 1 }

However, after rebuilding the cache and accessing some JSON fields via JSON:API, I don't see anything in the logs, so it seems like the class is not being picked up.