I'm not sure I find this wording to be really that much better. I would prefer a reference to the build section as opposed to Please see the above steps on how to do so. I would also like the Note to be separated out, not in parentheses after the previous statement.

I would also change the line Run the following command to run the tests. to maybe read:

Use npm test to run the tests.

No need to have a separate section for a single, two word command.

Also, sorry for the late response. We all appreciate your contribution! Thank you so much for taking the time to do this!