kubelet: detach probe workers from the pod sync context

Since PR 130487 probe workers inherit the pod worker's sync context via
probeManager.AddPod(ctx, pod). The pod worker cancels that context as
soon as a pod begins terminating, so every subsequent exec probe fails
with 'context canceled', doProbe discards the errored result, and the
pod's Ready condition stays frozen for the entire graceful termination.
Before PR 130487 the workers ran on context.Background() and readiness
probes kept working during shutdown.

Detach the workers' context with context.WithoutCancel, preserving the
logger and trace values. Worker lifecycle is unchanged: workers are
stopped explicitly via their stop channel (RemovePod/CleanupPods).