I managed to run it successfully by using require as shown below:

const fns = require('date-fns')

console.log(fns.format(new Date(), "'Today is a' eeee"))

Update:

I installed node v16.6.1 following the instructions in this answer and now I can run the following code successfully:

import { format } from 'date-fns';

console.log(format(new Date(), "yyyy-MM-dd'T'HH:mm:ss.SSS"));

As you can see, with moment lib, we need 2 steps to get the result: parse string to Date object, then format date object to string.

Your code - format(new Date("10-13-20"), 'MM-DD-YY') is format step, try convert a date object to a string with format template is MM-DD-YY. But your date object is not correct.

The solution is to do the same as with moment lib:

1. Parse date string to date object. Use parse

   const dateString = '10-13-20';
   const date = parse(dateString, 'MM-dd-yy', new Date()) // not MM-DD-YY
   

2. Format date object to result string. Use format

   const result = format(date, "yyyy-MM-dd'T'HH:mm:ss.SSSxxx")
   console.log(result)
   

   Result will be like (the same with moment's result in my timezone):

    2020-10-13T00:00:00.000+09:00