Is there a way to make JS Intl object to support classical Latin language?

Question

Intl object is great for all sorts for formatting. It supports basically all modern languages. But I can't make it work with classical Latin.

Can it be supported all? Passing 'la' as a locale doesn't seems to work.

I've tried this

new Intl.DateTimeFormat('la', {
    dateStyle: 'full',
    timeStyle: 'short'
}).format(new Date())

But it returned this: 'Wednesday, 8 November 2023 at 19:05'

The result is basically English.