How to parse in javascript locale date string to iso string for any format

Question

Let's say my default language in the browser is Ukrainian.

const dateStr = new Date().toLocaleString();
console.log(dateStr); //28.02.2024, 23:35:40 

Now I want to parse this dateStr back to Date;

const dateObj = new Date(dateStr);
// Invalid date

I know that I can use luxon.fromFormat for example, but then I should know the current string format for the locale. Is there way to pares any Locale String back to Date or ISO String?