add_new_custom_field.php

<?php
// Enter new field name
$fieldname = 'my_custom_field';

// Get the SC processor instance
$processor = $catalog->processor;

// Get the IM instance
$imanager = $catalog->imanager;

// Set the number of categories to be selected to 1000 or more
$processor->config->frontendCatPerPage = 1000;

// Get the SC categories and set 'section' parameter to 'frontend'
$catData = $processor->getCategories(
    ['section' => 'frontend']
);

// If the catData isn't null
if(isset($catData['total']) && $catData['total'] > 0) {
    foreach($catData['categories'] as $category) {

        // Get the FieldMapper instance and initialize the fields of the current category
        $fiedMapper = new FieldMapper();
        $fiedMapper->init($category->id);

        // Check if the field already exists.
        if(!$fiedMapper->fieldNameExists($fieldname)) {

            // Enter new field data you want to add to your categories
            $customField = new Field($category->id);
            $customField->name =    $fieldname;
            $customField->label =   'My Custom Field';
            $customField->type =    'text';
            $customField->position = null;
            $customField->default =  '';
            $customField->info =     'Put the field info here';
            $customField->required = null;
            $customField->minimum =  null;
            $customField->maximum =  null;

            // Save the field
            if($customField->save()) {
                echo 'The category '.$category->name.' got a new '.$customField->name.' field.<br>';
            }

        } else {
            echo 'The '.$category->name.' category already contains the '.$fieldname.' field.<br>';
        }
    }
} else {
    echo 'No categories found.<br>';
}