[Improve] Unify built-in and custom automations - #2451

​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.
• Stabilize deployment-wide automation settings tests and make telemetry-transition fixtures explicit against the seeded manager-stats default.

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.

The branch now includes current develop; the previously failing Test job passes on the resulting merge head. Browser proof was not rerun for the test-only CI stabilization change.