[serve] Clear `replica_updated_event` in streaming router to avoid blocking proxy event loop

[edoakes]

Why are these changes needed?

replica_updated_event was not being cleared. It seems that even though we were awaiting the event, it was not yielding the loop because the event was always set. This cause the while replica is not None loop to busy-spin, blocking the HTTP proxy event loop.

Closes https://github.com/ray-project/ray/issues/36460

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