JavaScript's standard API to get the runtime's default locale?

I'm not aware of a more straight-forward approach, but as you have already pointed out,

1. new Intl.NumberFormat().resolvedOptions().locale is a solution

2. DefaultLocale is an abstract operation, which might or might not be implemented in the future.

Hence, I would argue for polyfilling this function as:

if (typeof DefaultLocale === "undefined") {
    function DefaultLocale() {
        return new Intl.NumberFormat().resolvedOptions().locale;
    }
}

So, your code will reasonably assume the existence and call this function. In some point in the future, when this function is implemented in a standard manner, you will be able to clean up by removing the chunk from above.