Fix PTT screen grounding and canonical agent status

[Git-on-my-level]

Summary

• Keep every PTT screen answer bound to one locally owned, turn-scoped screenshot/report protocol.
• Close the voice turn from a verified local report or deterministic failure, instead of waiting for optional provider narration.
• Preserve the protocol through screenshot transport, report validation, persistence, playback ownership, errors, cancellation, and barge-in.
• Make canonical spawn acknowledgements and deterministic screen answers use the same authoritative output takeover path.

Product invariants affected

• INV-AGENT-*
• INV-CHAT-1
• INV-VOICE-1

Root cause

The screen report was accepted locally, but the reducer's generic tool-start path also set a provider-continuation obligation. The screen-report path presented a local result without discharging that obligation. When Gemini finished its provider turn with no further narration, the controller parked in awaitingResponse until the generic 20-second provider-response deadline. The live trace for turn 4645612F shows report_accepted at 00:07:35.587, provider_turn_done at 00:07:52.064, then cancellation at 00:08:12.528.

Durable guard

VoiceScreenEvidenceProtocolToken makes the screenshot/report handshake an explicit reducer-owned protocol tied to the original turn, screenshot effect, session, and epoch. Only a matching verified report may close it; enqueue failure, rejected report, provider terminal without a report, hub error, freshness expiry, cancellation, and barge-in all resolve the exact protocol fail-closed. Its deadline is the remaining five-second evidence lifetime, not the generic 20-second narration timeout. A stale deadline is rejected if its effect identity no longer matches the live state. The result remains fenced by persistence, playback, and journal completion; deterministic screen audio can preempt speculative native speech through the same output-lease ownership path used by canonical spawn acknowledgement.

Verification

• xcrun swift test --package-path desktop/macos/Desktop --skip-build --filter 'VoiceTurnOutputOwnershipTests|VoiceTurnReducerTests|RealtimeScreenEvidenceTests|VoiceTurnReducerFuzzTests' — 99 passed.
• xcrun swift test --package-path desktop/macos/Desktop --skip-build --filter 'VoiceTurnReducerTests|VoiceTurnCoordinatorTests|RealtimeScreenEvidenceTests|RealtimeHubSpawnAgentTests' — 130 passed.
• bash desktop/macos/scripts/agent-logic-harness.sh --cross-surface-smoke — 242 Swift agent-contract tests and 13 Rust retrieval-contract tests passed.
• python3 desktop/macos/scripts/check_desktop_test_quality.py — passed.
• git diff --check — passed.
• Independent Sol review — approved after adding the output-lease takeover regression.

Manual QA

Build and launch the existing /Applications/omi-qa-live-fix.app against development GCP. A PTT "what is on my screen" request should produce a current-screen answer or the deterministic verification failure within five seconds; it must not remain in a 20-second post-tool spinner. Barge-in remains silent unless there is an actionable failure.

[Git-on-my-level]

Monitor summary for PR #9775:

• No code changes were needed in this run: the context's unresolved trusted review thread list is empty, and a fresh review-thread scan found no unresolved inline comments.
• The previously reported cancelled Repo Checks were superseded by successful reruns.
• Verification: gh pr checks 9775 --repo BasedHardware/omi reports all active required checks passing or skipped; git diff --check origin/main...HEAD passed; python3 .github/scripts/check-desktop-changelog.py --base origin/main --head HEAD passed with a desktop changelog fragment present.