Why are these changes needed?

The Background agent test test_delivery_via_enqueue isn't reliable on the GitHub runner, likely due to some kind of resource contention.

test_delivery_via_enqueue verifies that a background agent's result reaches the orchestrator's LLM before the final reply. The wait_for_bg tool polls two signals, ctx.pending_messages (not yet drained) and DrainedModelRequest in stream history (already drained) - because _call_client drains the inbox before each LLM call, meaning the message can disappear from pending_messages before wait_for_bg runs. Both checks together cover both timing orderings of the asyncio race.

Similarly, the Network had two tests which relied on asyncio.sleep and have now been updated to be more deterministic.

Related issue number

N/A

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