[Fix] Custom automation results stay stale when user runs them now

[roomote-roomote]

​Opened on behalf of @daniel-lxs. Follow up by mentioning @roomote-roomote, in the web UI, or in Slack.

What changed

• Running a custom automation now refreshes its card immediately so persisted Last run and latest-result fields do not remain stale.
• Queued or launched Fast runs receive seven sparse, bounded follow-up refreshes through the existing ten-minute launch-claim recovery window, while completed and failed outcomes refresh only once.
• A mounted-state guard prevents late mutation callbacks from creating follow-up timers after the Run now button unmounts.
• Focused regression coverage exercises completed, failed, launched, queued, and unmount-before-resolution behavior.

Why this change was made

The Run now action only showed a toast, unlike adjacent custom-automation mutations that refresh the list. Immediate outcomes therefore stayed stale until reload, and queued Fast runs needed bounded follow-up because their durable result is recorded asynchronously after the mutation returns.

Impact

Custom automation cards now show persisted run metadata without requiring a reload. The change does not add indefinite polling, clears pending refresh timers when the button unmounts, and avoids creating new timers if the mutation resolves after navigation.

PR #2444 changes cadence rendering in the same component and later cadence-specific tests. This PR does not modify cadenceLabel or its call site; a synthetic merge-tree check against #2444 completed without conflicts after the lifecycle fix. Focused and full client coverage, web static checks, knip, and pre-push checks passed. The lifecycle fix has no visible mounted UI state to capture, so browser proof is not applicable to the updated head.

[roomote-community]

No new code issues found. See task

• Do not schedule follow-up refreshes after CustomAutomationRunButton unmounts (apps/web/src/components/settings/automations/CustomAutomationsSection.tsx:177).

_{Reviewed 60894a0}