Set Suitelet date field value based on the date format in user preference.

Client Script

let dateFormat = runtime.getCurrentUser().getPreference({
    name: 'DATEFORMAT'
});
let date = currentRec.getValue({
    fieldId: 'date'
});
let formattedDate = format.format({
    value: date,
    type: format.Type.DATE,
    format: dateFormat
});
document.location = url.resolveScript({
    scriptId: '<scriptid>',
    deploymentId: '<scriptdeploymentid>',
    params: {
        'clientScriptDate': formattedDate,
    }
});

Suitelet

let dateField = form.addField({
    id: 'date',
    label: 'Date',
    type: serverWidget.FieldType.DATE,
    container: '<container>'
});
let selectedDate = scriptContext.request.parameters.clientScriptDate;
dateField.defaultValue = selectedDate;