Background (run_in_background) subagents run detached from the main query loop, so their tool_use/tool_result never reached the desktop and their cards stayed on "no tool activity" even after completion. Route the activity through the SDK event queue as agent_tool_activity, re-emitted by the ws handler as tool_use_complete/tool_result tagged with the parent Agent tool_use id, so the UI groups them under the agent card like synchronous subagents.
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