end-to-end tests: make all `time.Sleep` context-aware

## Task summary

The end-to-end tests have been refactored to be context aware in order to cancel operations promptly when needed.

All `time.Sleep` usages should be changed to either:

- `context.WithTimeout(ctx, timeoutDuration)`
- timer + select case with context

so that sleeping operations get cancelled when the parent context gets canceled by an event.