dillon1000/react

Remove error code step from publish script (#18350)

Error codes don't need to be pulled from CI anymore because the ones
in source are already expected to match the build output.

I noticed this when running the 16.13.1 release. Patch releases are cut
with the commit used to build the previous release as a base. So the
publish script accidentally reverted the changes that had landed to
the error codes file since then.