WordPress Settings API Repeatable fields

It`s not the best solution but maybe it is helpful for you to create your own solution.

function display_ads_form_element()
{
    // get the total number of "advertising codes" from the database
    // the default value is 1
    $codes  = array('1' => '' );
    if( get_option('advertising_code') !== FALSE ) {
        $codes = get_option('advertising_code');
    }
    ?>

    <?php /// button to add the new field // ?>
    <input type="button" onClick="add_new_ad_code()" value="add new advertising code">

    <ul id="advertising_code_list" >

        <?php foreach($codes as $key => $code): ?>

            <?php /// create for every "advertising code" an input field // ?>
            <?php /// advertising_codes[key] => square brackets means the data will send as array  // ?>
            <?php /// data-listkey => is only an easy way that the js can detect the last key  // ?>
            <li><input type="text" name="advertising_code[<?php echo esc_attr( $key ); ?>]" value="<?php echo esc_attr( $code ); ?>" data-listkey="<?php echo esc_attr( $key ); ?>"/></li>

        <?php endforeach; ?>


    </ul>

    <script>

        function add_new_ad_code() {

            // detect the last li element
            const last_li = document.getElementById('advertising_code_list').lastElementChild;

            // get the listKey from the input field
            const new_key = parseInt(last_li.childNodes[0].dataset.listkey) + 1;

            // create the new list tag
            const li_element = document.createElement('li');

            // create the new input tag for the new advertising code
            const input_element = document.createElement('input');

            // set the type
            input_element.type = "text";

            // set the name attribute
            input_element.name = "advertising_code[" + new_key +  "]";

            // set empty value
            input_element.value = "";

            // add the new key as data attribute
            input_element.dataset.listkey = new_key;

            // add the new advertising code to the list element
            li_element.appendChild(input_element);

            // add the list element to the list
            document.getElementById('advertising_code_list').appendChild(li_element);
        }

    </script>

    <?php
}