I wasn't really happy with the Solutions I have found on the community for this issue.

With the old way of doing this (GlideappCalculationHelper.addItemToExistingRequest) you have to populate the variables manually after the requested item has been inserted. So here is a solution to add a catalog item to an existing requested item by using the CartJS API.

Script Include

var addCatalogItemToRequest = function (requestSysId, catItemMap, startFlow) {
    var tempCartName = "temp_" + gs.generateGUID();
    var tempCart = new sn_sc.CartJS(tempCartName);
    var cartItem = tempCart.addToCart(catItemMap).items[0];

    var cartItemHint = "<hints><entry key='sysparm_processing_hint' value='" +
        "setfield:request=" + requestSysId + "'/></hints>";

    var grCartItem = new GlideRecord("sc_cart_item");
    if (grCartItem.get(cartItem.cart_item_id)) {
        grCartItem.setValue("hints", cartItemHint);
        grCartItem.update();
    }
    //a business rule on sc_request will abort insert with these special_instructions
    tempCart.submitOrder({
        'special_instructions': '[__ABORT_INSERT_ACTION__]'
    });

    var getVars = function (grReqItem) {
        var vars = {};
        for (var n in grReqItem.variables) {
            vars[n] = grReqItem.variables[n];
        }
        return vars;
    };

    var grReqItem = new GlideRecord("sc_req_item");
    grReqItem.addEncodedQuery("request=" + requestSysId);
    grReqItem.orderByDesc("sys_created_on");
    grReqItem.setLimit(1);
    grReqItem.query();
    if (grReqItem.next()) {
        if (startFlow) {
            //as long as the OOTB business rules "Start Workflow" and "Start FlowDesigner Flow"
            //aren't modified setting the stage to "request_approved" should start the (work)flow
            grReqItem.stage = "request_approved";
            grReqItem.update();
        }
        return grReqItem;
    }
};

var requestId = 'd1eab3138741cd141820ed309bbb35b6'; //SysID of existing request
addCatalogItemToRequest(requestId, {
    'sysparm_id': 'd6ea58701b1c41105ff0c036464bcb73', //SysID of catalog item
    'sysparm_quantity': '1',
    'variables': { //variables of catalog item
        'type': 'Systemcopy',
        'selectdatetime_immediately': 'true',
        'additional_comments': 'testscript'
    }
});

Table: sc_requestWhen: Before insertOrder: 0

Condition: current.special_instructions == "[__ABORT_INSERT_ACTION__]"