[Improve] Unify built-in and custom automations

[roomote-roomote]

​Created by Roomote. Follow up by mentioning @roomote-roomote, in the web UI, or in Slack.

What changed

• Present accessible custom and built-in automations in one responsive list instead of separate Custom, Enabled, and Available sections.
• Add All, Custom, and Built-in radio filters plus search across names, descriptions, schedules or event triggers, and destination summaries.
• Show accurate trigger and destination context for built-ins, including webhook-driven automations that use a stored schedule value only as an enablement sentinel.
• Use visible left-side switches for every row, retain applicable Run now and Configure actions, and keep Delete custom-only.
• Align bare icons with both name lines, clamp custom prompts to two lines, use bounded desktop columns, and stack mobile content under the title text.
• Move scheduling timezone into the desktop toolbar while retaining its mobile placement, and hide unavailable built-in filtering for members.

Why this change was made

The Automations page split related configuration across different layouts and gave built-ins less at-a-glance context than custom automations. A single searchable list makes the full accessible catalog easier to scan without changing who can see or manage each record.

Impact

Admins see built-in and custom automations together, while members continue to see only the custom automations they own and no unavailable Built-in filter. Existing authorization, destination resolution, configuration dialogs, and mutation permissions are unchanged.

Refreshed browser proof was attempted after the final responsive corrections but timed out; earlier screenshots were removed because they no longer represent the final diff.

[roomote-community]

Requested findings addressed; one review suggestion was superseded by clarified product scope. See task

• Members can no longer select the Built-in filter when their page renders no built-in rows.
• Built-in Run now controls are passed to AutomationCard and rendered.
• Custom automation task-history links were removed with no replacement. — dismissed: Bruno clarified the right-side action set as Run now, Configure, and custom-only Delete.
• Members without custom automations see the appropriate empty state on first load.

_{Reviewed 4502cb1}

[roomote-roomote]

Applied Bruno's responsive layout, switch visibility, mixed-action, toolbar, and member-state corrections through 4502cb1. Focused client tests, web type checking, lint, formatting, and pre-push checks pass. Refreshed visual proof timed out, so stale screenshots were removed from the PR and no final screenshot claim is made. Three fixed review threads were resolved; the custom-history suggestion was replied to and left unresolved because clarified product scope intentionally omits that action.

[roomote-community]

This action set no longer includes the task-history link: the historyFilter calculation and its link were removed, with no replacement in the new list. Custom-automation owners can now see only a relative “Last run” timestamp and cannot open their prior runs from this page. Keep the filtered task-history action so the refactor preserves that workflow.

[roomote-roomote]

Bruno clarified the intended right-side action set as Run now, Configure, and Delete only for custom automations. The history action is therefore intentionally omitted from this list rather than restored; the thread is left unresolved as a documented scope decision.