feat: background tasks

Adds Background Tasks — recurring background agents the user can set up to
either keep a digest current (daily email summary, top HN stories, weather
brief) or perform a recurring action (draft a reply, post to Slack, call an
API). Each task is a persistent set of instructions plus optional triggers
(schedule, time-of-day window, or matching incoming Gmail / calendar event).
The agent reads the verbs in the instructions on every run and picks the
right mode automatically.

User-facing surfaces:
- New "Background tasks" entry in the sidebar, with a table listing every
  task, its schedule, last run, and an active toggle.
- A detail page per task with a max-width reader showing the task's
  current output and a control sidebar for editing instructions, triggers,
  and reviewing run history.
- "New task" can open in a free-form box where the user describes what they
  want and Copilot sets it up end-to-end, or in a structured form for
  manual setup.
- "Edit with Copilot" hand-off from the detail view, pre-seeded with the
  task's context.

Under the hood:
- The event pipeline that previously powered live-notes is now a generic
  consumer registry. Live-notes and background tasks both subscribe;
  incoming events are routed to candidates from both concurrently.
- Schedule helpers and the agent-message trigger block are factored out of
  live-notes into shared modules. Both features use the same building
  blocks now.
- Copilot's proactive routing is reframed: anything recurring (cadence
  words, watch / monitor verbs, action verbs, event-conditional asks) now
  flows to background tasks. Live-notes load only on explicit mention.
- A small reliability fix for the run-creation fallback chain: an
  empty-string model/provider passed by an LLM tool call now correctly
  falls through to the default instead of being persisted as a real value.

Co-Authored-By: Claude Opus 4.7 (1M context) <noreply@anthropic.com>

apps/x/packages/shared/src/runs.ts

@@ -26,6 +26,7 @@ export const StartEvent = BaseRunEvent.extend({
     useCase: z.enum([
         "copilot_chat",
         "live_note_agent",
+        "background_task_agent",
         "meeting_note",
         "knowledge_sync",
     ]).optional(),
@@ -138,6 +139,7 @@ export const AskHumanResponsePayload = AskHumanResponseEvent.pick({
 export const UseCase = z.enum([
     "copilot_chat",
     "live_note_agent",
+    "background_task_agent",
     "meeting_note",
     "knowledge_sync",
 ]);