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
   

<script type="module">
  import { format } from 'https://esm.run/date-fns'

  const date = new Date('Jul-30-2021');

  console.log(date);

  console.log(format(date, 'MMM-dd-yyyy, mm:HH:ss'));
</script>

Now you can apply the date-fns format(date, 'MMM-dd-yyyy')

Your pattern is not correct e.g. you need

1. y instead of Y
2. d instead of D
3. H instead of h

etc. Check this page to learn more about these letters.

Demo:

const fns = require('date-fns')

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

Output from a sample run:

2021-08-03T19:43:08.891

ONLINE DEMO

(Note: Click Console on the bottom right of the ONLINE DEMO page.)

(Also what is the 'T' for? Just to specify that a time measurement will follow?

Correct. It is a separator for date and time as per ISO-8601 standards.