test: remove internal errorCache property

The internal `assert` modules `errorCache` property is exposed only for
testing. The one test that used it is rewritten here to not use it.

This has the following advantages:

* The test now makes sure that there is an empty cache in a more robust
  way. Instead of relying on the internal implementation of
  `errorCache`, it simply spawns a separate process.
* One less test using the `--expose-internals` flag.

PR-URL: https://github.com/nodejs/node/pull/23304


Reviewed-By: Ruben Bridgewater <ruben@bridgewater.de>
Reviewed-By: Sakthipriyan Vairamani <thechargingvolcano@gmail.com>