我刚刚测试了您的代码，我想您的javascript中的ajaxurl是错误的，它一定是：

<?php echo admin_url( \'options.php\' ); ?>

class TestAjaxSettingsAPI {
    public function __construct() {
        add_action( \'admin_menu\', array( $this, \'agy_admin_menu\' ) );
        add_action( \'admin_init\', array( $this, \'agy_register_settings\') );
    }

    public function agy_admin_menu() {
        add_menu_page( \'Agy menu\', \'Agy menu\', \'manage_options\', \'agy-menu\', array( $this, \'agy_dashboard_page\' ), \'\', 99 );
    }

    public function agy_dashboard_page() {
        ?>
        <form id="agy-form-submit" action="options.php" method="post">
    
            <?php
            settings_errors( \'agy_settings_fields\' );
            wp_nonce_field( \'agy_dashboard_save\', \'agy_form_save_name\' ); // CHECK THIS AT THE END
            settings_fields( \'agy_settings_fields\' );
            ?>
    
            <div id="agy-tab1" class="agy-tabcontent">
                <?php do_settings_sections( \'agy_settings_section_tab1\' ); ?>
            </div>
    
            <?php
            submit_button(
                __( \'Save Changes\', \'agy\' ),
                \'\',
                \'agy_save_changes_btn\',
                true,
                array( \'id\' => \'agy-save-changes-btn\' )
            );
    
            if ( wp_doing_ajax() ) {
                wp_die();
            }
            ?>
    
        </form>

        <script>
            function agyAjaxSubmit() {
                var agyFormData = new FormData(this);

                agyFormData.append(\'agy_save_changes_btn\', 1);
                // agyFormData.append(\'security\', agy_public_ajax.agy_publisher_name);

                jQuery.ajax({
                    type: \'POST\',
                    url: \'<?php echo admin_url( \'options.php\' ); ?>\',
                    data: agyFormData,
                    processData: false,
                    contentType: false,
                    success: function () {
                        console.log(\'work\');
                    },
                    error: function () {
                        console.log(\'not work\');
                    }
                });

                return false;
            }

            jQuery(\'#agy-form-submit\').submit(agyAjaxSubmit);
        </script>
    
        <?php
        if ( ! isset( $_POST[\'agy_form_save_name\'] ) ||
             ! wp_verify_nonce( $_POST[\'agy_form_save_name\'], \'agy_dashboard_save\' ) ) {
            return;
        }
        ?>
       
        <?php
    }

    public function agy_settings_section_callback() {}

    public function agy_section_id_enabled_disabled() {
        // get the value of the setting we\'ve registered with register_setting()
        $setting = get_option(\'agy_settings_fields\');
        // output the field
        ?>
        <input type="text" name="agy_settings_fields" value="<?php echo isset( $setting ) ? esc_attr( $setting ) : \'\'; ?>">
        <?php
    }

    public function agy_register_settings() {

        register_setting( \'agy_settings_fields\', \'agy_settings_fields\' );
    
        // Adding sections
        add_settings_section( \'agy_section_id\', __( \'General\', \'agy\' ), array(
            $this,
            \'agy_settings_section_callback\'
        ), \'agy_settings_section_tab1\' );
    
        add_settings_field( \'agy_section_id_enabled_disabled\', __( \'Enable / Disable\', \'agy\' ), array(
            $this,
            \'agy_section_id_enabled_disabled\'
        ), \'agy_settings_section_tab1\', \'agy_section_id\' );
    }
}

new TestAjaxSettingsAPI();