fix(background-agent): suppress redundant parent wakes during gate hold

[code-yeongyu]

Summary

• Suppress redundant background-agent parent wakes while the promptAsync gate is still holding the already-dispatched wake.
• Preserve meaningful follow-up wakes: new notification content, reply-mode upgrades, and prompt-context changes still requeue and dispatch after the hold.

Root Cause

The parent wake notifier tracked the last dispatched wake, but the same-source reserved-path check only suppressed byte-for-byte identical pending wake arrays. Duplicate background completion edges could collect repeated copies of the already-dispatched notification during the post-dispatch hold, turning ["wake A"] into ["wake A", "wake A"]. Strict equality treated that as new work, requeued it, and launched a second internal parent prompt after the hold released.

Changes

• Replace strict same-wake comparison with redundant-wake coverage semantics.
• Add regression coverage for redundant duplicate bursts.
• Add boundary coverage proving reply upgrades and prompt-context changes are preserved.

Testing

• bun test src/features/background-agent/parent-wake-same-source-requeue.test.ts - 6 pass, 0 fail, 41 expectations.
• bun test src/features/background-agent/parent-wake-same-source-requeue.test.ts src/features/background-agent/parent-wake-active-turn-event.test.ts src/features/background-agent/parent-wake-user-message-race.test.ts src/features/background-agent/task-completion-cleanup.test.ts src/shared/prompt-async-route-audit.test.ts - 52 pass, 0 fail, 176 expectations.
• bun run typecheck - pass.
• bun run build - pass.
• bun test > /tmp/omo-bugfix-bun-test-after-merge.log 2>&1 - exit 0, 3,401 pass lines, no fail/error lines.

Evidence

• Investigated live session ses_1ace82b4dffeDeez3U2yA4eONr and child sessions from the transcript/logs.
• Updated sibling OpenCode checkout with git fetch --all --prune && git pull --ff-only; current OpenCode promptAsync still returns before the prompt run durably settles.
• Git history/blame identifies the relevant sequence: same-source requeue in 11d2cfb8a and strict duplicate suppression in 560569e36.

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Summary by cubic

Prevents duplicate parent prompts by suppressing redundant background-agent wakes while promptAsync holds a reservation. Keeps meaningful follow-ups (new notifications, reply upgrades, and prompt-context changes) so they dispatch after the hold.

• Bug Fixes
  • Switch from strict equality to redundancy coverage: same prompt context, reply mode coverage, and notification subset.
  • Suppress duplicate bursts collected during the hold to avoid a second parent prompt.
  • Preserve meaningful changes and add regression tests for duplicates and upgrades.

^{Written for commit 1023841. Summary will update on new commits. Review in cubic}

[code-yeongyu]

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