What I want to do

I want to realize this on Drupal9.

• Finally,I want to create the custom field on a webform.
• With this custom field,Submitter who use the webform can add a new taxonomy term to a vocabulary (This vacabulary is predetermined in module) on this webform.
• This field is text field.
• If the new term already exits in the vocaburaly,it isn't added to the vocabulary.
• If it is possible,the submitter can also choose a term from the terms which is already registered.

Problem

I am trying custom field which can register a term in a content type. (I can't add custom field to webform.So,I tried it first.) I already created it tentatively.However,if I write something to this field,a warning is output.

Warning: Array to string conversion in Drupal\mymodule2\Plugin\Field\FieldType\MyModule2Field->isEmpty() (line 62 of modules/custom/mymodule2/src/Plugin/Field/FieldType/MyModule2Field.php).

MyModule2 is the custom module which I created.

So I want to know how to create a custom field which can register a term properly.

Code and Folder Structure

mymodule2(folder) -mymodule2.info.yml

-mymodule2.module

-src(folder)/Plugin(folder)/Field(folder)

Field(folder)-FieldType(folder)-MyModule2Field.php

Field(folder)-FieldWidget(folder)-MyModule2Widget.php

Field(folder)-FieldFormatter(folder)-MyModule2Formatter.php

Codes

mymodule2.info.yml

name: mymodule2
type: module
description: hogehoge
core_version_requirement: ^8.8 || ^9
package: Example

mymodule2.module

<?php ?>

MyModule2Field.php

    <?php 
namespace Drupal\mymodule2\Plugin\Field\FieldType;

use Drupal\Core\Field\FieldItemBase;
use Drupal\Core\Field\FieldStorageDefinitionInterface;
use Drupal\Core\TypedData\DataDefinition;
use Drupal\Core\StringTranslation\TranslatableMarkup;
use Drupal\taxonomy\Entity\Term;      
use Drupal\Core\Link;
use Drupal\Core\Url;
/**
 * Plugin implementation of the 'MyModule2' field type.
 *
 * @FieldType(
 *   id = "mymodule2",
 *   label = @Translation("MyModule"),
 *   description = @Translation("This field is used to store alpha-numeric values."),
 *   default_widget = "MyModule2Widget",
 *   default_formatter = "MyModule2Formatter"
 * )
 */
class MyModule2Field extends FieldItemBase {
 
 /**
  * {@inheritdoc}
  */
  
  public static function propertyDefinitions(FieldStorageDefinitionInterface $definition) {
    // Prevent early t() calls by using the TranslatableMarkup.
    $properties['mymodule2'] = DataDefinition::create('string')
    ->setLabel(new TranslatableMarkup('Text value'));
 
    return $properties;
  }
 
  /**
   * {@inheritdoc}
   */
  public static function schema(FieldStorageDefinitionInterface $definition) {
    $schema = [
        'columns' => [
          'mymodule2' => [
            'type' => 'varchar',
            'length' => 255,
          ],
        ],
    ];
    
    
    
    return $schema;
  }
 
  /**
   * {@inheritdoc}
   */
  public function isEmpty() {
    $value = $this->getValue();
    if (isset($value['mymodule2']) && $value['mymodule2'] != '') {
      
      /*this is problem code*/
      $val=implode("",$value);
      $arr = explode(',',$val);
      $categories_vocabulary='pixelarttag';
      foreach($arr as $a){
        $term = term::create(array(
        'parent' => array(),
        'name' => $a,
        'vid' => $categories_vocabulary,))->save();
      }
      return FALSE;
    }
    return TRUE;
  }
 
}
?>

MyModule2Widget.php

<?php 
namespace Drupal\mymodule2\Plugin\Field\FieldWidget;
 
use Drupal\Core\Field\FieldItemListInterface;
use Drupal\Core\Field\WidgetBase;
use Drupal\Core\Form\FormStateInterface;
 
/**
 * Plugin implementation of the 'MyModule2Widget' widget.
 *
 * @FieldWidget(
 *   id = "MyModule2Widget",
 *   label = @Translation("My Field widget"),
 *   field_types = {
 *     "mymodule2"
 *   }
 * )
 */
class MyModule2Widget extends WidgetBase {
 
 /**
   * {@inheritdoc}
   */
  public function formElement(FieldItemListInterface $items, $delta, array $element, array &$form, FormStateInterface $form_state) {
   
    $element['mymodule2'] =  [
      '#type' => 'textfield',
      '#title' => 'AddictionTaxonomy',
      '#description' => 'Custom field to be used for alpha-numeric values',
      '#default_value' => isset($items[$delta]->title) ? $items[$delta]->title : NULL,
      '#weight' => 0,
    ];
 
    return $element;
  }
 
}
?>

MyModule2Formatter.php

<?php
namespace Drupal\mymodule2\Plugin\Field\FieldFormatter;
 
use Drupal\Core\Field\FormatterBase;
use Drupal\Core\Field\FieldItemListInterface;
 
/**
 * Plugin implementation of the 'MyModule2Formatter' formatter.
 *
 * @FieldFormatter(
 *   id = "MyModule2Formatter",
 *   label = @Translation("My Field Formatter"),
 *   field_types = {
 *     "mymodule2"
 *   }
 * )
 */
class MyModule2Formatter extends FormatterBase {
 
 /**
   * {@inheritdoc}
   */
  public static function defaultSettings() {
    return [
      // Implement default settings.
    ] + parent::defaultSettings();
  }
 
  /**
   * {@inheritdoc}
   */
  public function settingsSummary() {
    $summary = [];
    $summary[] = $this->t('Displays the random string.');
    return $summary;
  }
 
  /**
   * {@inheritdoc}
   */
  public function viewElements(FieldItemListInterface $items, $langcode) {
 
    $elements = [];
    foreach ($items as $delta => $item) {
      $elements[$delta] = [
        '#type' => 'markup',
        '#markup' => $item->mymodule2
      ];
    }
 
    return $elements;
  }
}
?>

P.S.

I am not good at English, and I also do not know much about Drupal.I have studied Drupal since 1 month ago.So,I might ask something stupid.Please forgive me

Sincerely