Reduce integration test overhead (#32475)

Reduce integration test overhead (#32475)

In profiling integration tests, I found a couple places where per-test
overhead could be reduced:

* Avoiding disk IO by synchronizing instead of deleting & copying test
Git repository data. This saves ~100ms per test on my machine
* When flushing queues in `PrintCurrentTest`, invoke `FlushWithContext`
in a parallel.

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Co-authored-by: wxiaoguang <wxiaoguang@gmail.com>