Custom field in Customer Registration form

In the User Registration form I want to add a custom text field where the user can fill in a role(or any other text)

I’m using these 2 functions to display the field and then save it to the User. Right now the field displays but the billing_role doesn’t get saved to the User.

I’m testing this in another function where all the User data gets shown

<?php
function wooc_extra_register_fields() {
    $billing_role = ! empty( $_POST['billing_role'] ) ? intval( $_POST['billing_role'] ) : '';
    ?>
       <p class="form-row form-row-wide">
       <label for="billing_role"><?php _e( 'billing_role', 'woocommerce' ); ?></label>
       <input type="text" class="input-text" name="billing_role" id="billing_role" value="<?php echo esc_attr( $billing_role ); ?>" />
       

       <div class="clear"></div>
       <?php
 }
 add_action( 'woocommerce_register_form_start', 'wooc_extra_register_fields' );

/**
* save extra field.
*/
function wooc_save_extra_register_fields($customer_id) {
	echo $customer_id;
    if ( ! empty( $_POST['billing_role'] ) ) {
        update_user_meta( $customer_id, 'billing_role', sanitize_text_field( $_POST['billing_role'] ) );
    }
}
add_action( 'woocommerce_created_customer', 'wooc_save_extra_register_fields' );

What is the correct way to do this? Thanks in advance