[test]: de-flake client-cache.original.test.ts (#84831)
This has been frequently flaking on deployment tests
([ex](https://github.com/vercel/next.js/actions/runs/18420977957/job/52496287125))
- refactored from deprecated `check` to `retry`
- added more explicit waitForElement signals before proceeding in the
test flow
Validated the change by running it 6 times locally.
Test run:
https://github.com/vercel/next.js/actions/runs/18470261924/job/52637178224
