Improved

// Function to add new fields to WP tags
function custom_tag_fields($term) {
    // Get term meta data
    $term_metas = [
        'entity_name' => get_term_meta($term->term_id, 'entity_name', true),
        'google_entity_url' => get_term_meta($term->term_id, 'google_entity_url', true),
        'wikipedia_url' => get_term_meta($term->term_id, 'wikipedia_url', true),
        'wikidata_url' => get_term_meta($term->term_id, 'wikidata_url', true)
    ];

    // Fields to add
    $fields = [
        'entity_name' => 'Entity Name',
        'google_entity_url' => 'Google Entity URL',
        'wikipedia_url' => 'Wikipedia URL',
        'wikidata_url' => 'Wikidata URL'
    ];

    foreach ($fields as $field_id => $label) {
        ?>
        <tr class="form-field">
            <th scope="row" valign="top"><label for="<?php echo $field_id; ?>"><?php _e($label); ?></label></th>
            <td>
                <input type="text" name="<?php echo $field_id; ?>" id="<?php echo $field_id; ?>" value="<?php echo esc_attr($term_metas[$field_id]); ?>">
            </td>
        </tr>
        <?php
    }
}
add_action('post_tag_edit_form_fields', 'custom_tag_fields');

// Function to save the new custom fields data
function save_custom_tag_fields($term_id) {
    // Fields to save
    $fields = [
        'entity_name' => 'sanitize_text_field',
        'google_entity_url' => 'esc_url_raw',
        'wikipedia_url' => 'esc_url_raw',
        'wikidata_url' => 'esc_url_raw'
    ];

    foreach ($fields as $field_id => $sanitize_func) {
        if (isset($_POST[$field_id])) {
            update_term_meta($term_id, $field_id, $sanitize_func($_POST[$field_id]));
        }
    }
}
add_action('edited_post_tag', 'save_custom_tag_fields');

// Function to add schema to the posts and tag pages
function add_sameAs_schema_rank_math( $data, $jsonld ) {
    if(is_single() || is_tag()) {
        global $post;
        $post_tags = wp_get_post_tags($post->ID);

        if (!empty($post_tags)) {
            foreach ($post_tags as $tag) {
                $entity_name = get_term_meta($tag->term_id, 'entity_name', true);
                $sameAs_array = array_filter([
                    get_term_meta($tag->term_id, 'google_entity_url', true),
                    get_term_meta($tag->term_id, 'wikipedia_url', true),
                    get_term_meta($tag->term_id, 'wikidata_url', true)
                ]); // Remove empty elements

                if (!empty($entity_name) && !empty($sameAs_array)) {
                    // Create schema array
                    $schema = [
                        "@type" => "Thing",
                        "name" => $entity_name,
                        "sameAs" => $sameAs_array
                    ];
                    // Add to Article schema on single posts
                    if(is_single() && isset($data['Article'])) {
                        $data['Article']['about'][] = $schema;
                    }
                    // Add to CollectionPage schema on tag pages
                    if(is_tag() && isset($data['CollectionPage'])) {
                        $data['CollectionPage']['about'][] = $schema;
                    }
                }
            }
        }
    }
    return $data;
}
add_filter( 'rank_math/json_ld', 'add_sameAs_schema_rank_math', 10, 2 );