fix(mobile): stop false "task failed" notifications for stale/cancelled runs

[k11kirky]

Problem

As a user of both the desktop and mobile apps, you frequently get "XYZ failed" push notifications from mobile for tasks that are stale with no activity — tasks that didn't fail, you'd simply finished with them.

The "XYZ failed" body is produced in taskSessionStore.maybePresentLocalNotification, fired from the terminal-status branch of _handleCloudUpdate. Two design choices combined to cause false alerts:

1. cancelled was mislabeled as failed. mapTerminalStatus collapsed the backend cancelled status into failed. When a cloud sandbox is stopped/reaped after you finish with a task, the run goes cancelled — and the app showed "Run failed" and pushed "XYZ failed". (A genuine user cancel mid-turn comes back as _posthog/turn_complete, so cancelled as a run status overwhelmingly means "stopped", not "failed".)

2. Stale reconnects re-fired the notification. By design, snapshots don't clear awaitingPing so the terminal-status block can own the terminal ping. But it didn't distinguish recent from long-ago: reconnecting to a run that ended while you were away, with awaitingPing still armed from your last prompt, re-fired "XYZ failed" for something you finished with hours earlier.

Changes

• mapTerminalStatus keeps cancelled as a distinct terminal state instead of collapsing it into failed. Cancelled runs now show a neutral "Run stopped" banner (success styling, "Continue" action) and never fire a failure notification.
• Thread the run's updated_at (already tracked as watcher.lastStatusUpdatedAt) through status/snapshot updates as statusUpdatedAt, and suppress the terminal ping when the transition is older than 2 minutes. A missing/unparseable timestamp is treated as fresh, so genuine just-happened terminal alerts are never suppressed.
• The live logs path (a _posthog/error arriving while you're actively waiting) is unchanged — that's a real, just-happened failure and still notifies.
• Extracted the terminal banner into a small TerminalStatusBanner component to cleanly handle the three states.

Frontend behavior change (no screenshot — node/vitest env): cancelled runs render "Run stopped" instead of "Run failed".

How did you test this?

• Added taskSessionStore.test.ts (5 cases): no ping for a cancelled run, ping for a recent failed run, no ping for a stale failed run (reconnect snapshot), no ping when not awaiting a ping, and a completion ping. All pass.
• npx vitest run src/features/tasks → 20 files / 75 tests pass.
• npx tsc --noEmit clean for all changed source files; biome check clean on changed files. (Pre-existing, unrelated tsc errors remain from test-infra typings and the unbuilt @posthog/shared package.)

Automatic notifications

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

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