fix(parent-wake): reuse prompt gate assistant blocking

[SpencerJung]

Summary

• Reuse the shared prompt-async-gate assistant-turn predicate before dispatching parent wake prompts.
• Prevent parent wakes from injecting while the latest assistant response is still streaming or has finish: unknown.
• Add regression coverage for stale-idle parent wake dispatch with an unknown/streaming assistant turn.

Changes

• Export latestAssistantTurnBlocksInternalPrompt from the shared prompt gate.
• Use it in ParentWakeNotifier instead of the narrower tool-wait-only check.
• Extend parent-wake race tests for non-tool incomplete assistant turns.

Testing

bun test packages/ast-grep-mcp/src/sg-cli-path.test.ts src/features/background-agent/parent-wake-user-message-race.test.ts src/features/background-agent/parent-wake-active-turn-event.test.ts src/features/background-agent/parent-wake-same-source-requeue.test.ts src/hooks/todo-continuation-enforcer/todo-continuation-enforcer.test.ts src/cli/run/output-renderer.test.ts src/shared/agent-display-names.test.ts
bun run typecheck
bun run build

Related Issues

Refs #4164
Refs #4167
Refs #4169

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Summary by cubic

Blocks parent wake prompts when the latest assistant turn is incomplete (tool wait, streaming, or finish: unknown) by reusing the shared prompt gate predicate. Fixes a race that injected parent wakes while an assistant response was still in progress (refs #4164, #4167, #4169).

• Bug Fixes
  • Exported and reused latestAssistantTurnBlocksInternalPrompt in ParentWakeNotifier (replaces tool-wait-only check).
  • Updated log message to reflect generic “blocks internal prompts” state.
  • Added tests for unknown/streaming assistant finishes and extended parent-wake race coverage.

^{Written for commit f217603. Summary will update on new commits. Review in cubic}

[cubic-dev-ai]

No issues found across 3 files

Confidence score: 5/5

• Automated review surfaced no issues in the provided summaries.
• No files require special attention.

<sub>Auto-approved: This change replaces a tool-wait-only check with the same shared predicate already used in the prompt gate, adding a test for the missing streaming/unknown finish case, so the logic is strictly more correct and cannot introduce regressions.

Re-trigger cubic</sub>