fix(sessions): notify cloud turn completions in either log order

[charlesvien]

Problem

Since #3572, desktop notifications for cloud task completions only fire when _posthog/turn_complete happens to land before the session/prompt response in the log stream. The two writes race in the agent's log stream, so roughly half of all cloud completions never notify at all: no banner, no sound, not even later.

The completedActiveTurn gate from #3572 treats a turn as already notified once currentPromptId is cleared, but the prompt response also clears it. When the response lands first, the turn is disarmed before turn_complete arrives and the notification is suppressed. The old comment claiming "Cloud sessions never see that response" is wrong: the agent taps both directions of the ACP stream into the log, and a survey of 33 completed turns in real session logs found 14 with the response first and 19 with turn_complete first.

Note: this is one of two issues behind the "notifs don't fire until I refocus the app" report. The other (notifications bursting on refocus instead of arriving while the app is backgrounded) is a delivery stall around App Nap and the cloud watcher's permanent give-up, and needs a separate fix.

Changes

Cloud sessions no longer disarm the turn on the session/prompt response; only _posthog/turn_complete does. The response still clears isPromptPending, so spinner behavior is unchanged, and local sessions are untouched. The turn_complete handler now reads the entry's real stopReason instead of hardcoding end_turn, so cancelled or failed turns no longer ring or speak "done". Keeping the turn start time intact until turn_complete also fixes completion sound duration scaling for cloud tasks, which the response previously wiped.

How did you test this?

• New parameterised cases in cloudTaskUpdateNotifications.test.ts: response before and after turn_complete, duplicate turn_complete after a response-first turn, multi-turn with mixed orderings, a cancelled turn and a duration assertion.
• Red/green verified: the response-first cases fail on main's sessionService.ts (4 failures) and pass with the fix.
• @posthog/core: full suite (2490 tests), typecheck and biome lint clean. @posthog/ui: sessions and notifications suites (542 tests) pass after updating one hydration test that encoded the old disarm behavior; workspace typecheck clean.

Automatic notifications

• Publish to changelog?
• Alert Sales and Marketing teams?

[trunk-io]

😎 Merged successfully - details.

[github-actions]

React Doctor found no issues in the changed files. 🎉

_{Reviewed by React Doctor for commit e72ba82.}

[greptile-apps]

_{Reviews (1): Last reviewed commit: "keep cloud turn armed until turn_complet..." | Re-trigger Greptile}

[richardsolomou]

my b

[greptile-apps]

_{Reviews (2): Last reviewed commit: "keep cloud turn armed until turn_complet..." | Re-trigger Greptile}

[richardsolomou]

meep

[k11kirky]

/trunk merge