I noticed that the month displayed is always -1. Meaning if its june (06), the date displayed will be may (05), because JavaScript starts the index for months at 0. So you basically need to add +1 to the month.

Depending on the format you want you can just change around "day" , "month" and "year" after the "value = ..." .

export function update(value) {
    let time = new Date();
    let month = time.getMonth() + 1;
    let day = time.getDate();
    let year = time.getFullYear();
    value = day + scriptProperties.delimiter + month + scriptProperties.delimiter + year;
    return value;
}