templates/stage-cypress-tests: Prevent race condition with support file

Sometimes when multiple cypress processes load the same support file in parallel, a race condition is encountered as file copy operations are performed. As a result, the content of the support file is not loaded and cypress tests will fail (see this job for instance).

So use a specific copy of the support file for each cypress runner to mitigate that issue.

---

Migrated from D8782 (view on Phabricator)