[JS][Release] Stop re-testing JS packages when uploading to npm

### Describe the enhancement requested

As part of the release process we test all the packages on several CI jobs for different OS and environments.

We also do a lot of integration tests and release verification.

As part of the release verification we do test JS packages.

Once the release has been approved we are executing the [npm-release.sh](https://github.com/apache/arrow/blob/main/js/npm-release.sh#L21-L23) where we re-test again JS.

JS is the only package were once the release is approved we test again. Is this really necessary?

The post-release task for JS could be reduced if we avoid testing which feels unnecessary at this point.

### Component(s)

JavaScript, Release