test: refactor test-http-client-timeout-option-with-agent

* Switch from Date.now() to process.hrtime.bigint().
* Move start time recording to before the request is created, not after.

Fixes: https://github.com/nodejs/node/issues/25746

PR-URL: https://github.com/nodejs/node/pull/25752


Reviewed-By: Gus Caplan <me@gus.host>
Reviewed-By: James M Snell <jasnell@gmail.com>