test: make contexthelper timeout tests deterministic

[tsj-30]

What type of PR is this?
/kind flake

What this PR does / why we need it:
Makes context timeout handling and tests deterministic by avoiding logging from a goroutine, safely stopping/draining timers, waiting for goroutine completion in cleanup, and waiting for actual context cancellation in tests to reduce flakiness.

Which issue(s) this PR is related to:
N/A

Special notes for your reviewer:
Stabilizes contexthelper_test.go by replacing time-based sleeps with cancellation-based waits; reduces timing-related flakes.

Does this PR introduce a user-facing change?
NONE

https://prow.k8s.io/view/gs/kubernetes-ci-logs/logs/ci-kubernetes-unit-ppc64le/1994147797376438272
Flake

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[k8s-ci-robot]

[APPROVALNOTIFIER] This PR is NOT APPROVED

This pull-request has been approved by: tsj-30
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