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/ipc.ts

@@ -7,6 +7,12 @@ import { AgentScheduleConfig, AgentScheduleEntry } from './agent-schedule.js';
 import { AgentScheduleState } from './agent-schedule-state.js';
 import { ServiceEvent } from './service-events.js';
 import { LiveNoteAgentEvent, LiveNoteSchema } from './live-note.js';
+import {
+    BackgroundTaskAgentEvent,
+    BackgroundTaskSchema,
+    BackgroundTaskSummarySchema,
+    TriggersSchema,
+} from './background-task.js';
 import { UserMessageContent } from './message.js';
 import { RowboatApiConfig } from './rowboat-account.js';
 import { ZListToolkitsResponse } from './composio.js';
@@ -218,6 +224,10 @@ const ipcSchemas = {
     req: LiveNoteAgentEvent,
     res: z.null(),
   },
+  'bg-task-agent:events': {
+    req: BackgroundTaskAgentEvent,
+    res: z.null(),
+  },
   'models:list': {
     req: z.null(),
     res: z.object({
@@ -691,6 +701,95 @@ const ipcSchemas = {
       })),
     }),
   },
+  // Background-task channels
+  'bg-task:run': {
+    req: z.object({
+      slug: z.string(),
+      context: z.string().optional(),
+    }),
+    res: z.object({
+      success: z.boolean(),
+      runId: z.string().nullable().optional(),
+      summary: z.string().nullable().optional(),
+      error: z.string().optional(),
+    }),
+  },
+  'bg-task:get': {
+    req: z.object({
+      slug: z.string(),
+    }),
+    res: z.object({
+      success: z.boolean(),
+      task: BackgroundTaskSchema.nullable().optional(),
+      error: z.string().optional(),
+    }),
+  },
+  'bg-task:patch': {
+    req: z.object({
+      slug: z.string(),
+      partial: BackgroundTaskSchema.partial(),
+    }),
+    res: z.object({
+      success: z.boolean(),
+      task: BackgroundTaskSchema.nullable().optional(),
+      error: z.string().optional(),
+    }),
+  },
+  'bg-task:create': {
+    req: z.object({
+      name: z.string(),
+      instructions: z.string(),
+      triggers: TriggersSchema.optional(),
+      model: z.string().optional(),
+      provider: z.string().optional(),
+    }),
+    res: z.object({
+      success: z.boolean(),
+      slug: z.string().optional(),
+      error: z.string().optional(),
+    }),
+  },
+  'bg-task:delete': {
+    req: z.object({
+      slug: z.string(),
+    }),
+    res: z.object({
+      success: z.boolean(),
+      error: z.string().optional(),
+    }),
+  },
+  'bg-task:stop': {
+    req: z.object({
+      slug: z.string(),
+    }),
+    res: z.object({
+      success: z.boolean(),
+      error: z.string().optional(),
+    }),
+  },
+  'bg-task:list': {
+    req: z.object({
+      offset: z.number().int().nonnegative().optional(),
+      limit: z.number().int().positive().optional(),
+      sort: z.enum(['createdAt:desc', 'createdAt:asc', 'name:asc']).optional(),
+    }),
+    res: z.object({
+      items: z.array(BackgroundTaskSummarySchema),
+      total: z.number().int().nonnegative(),
+    }),
+  },
+  // Returns the runIds recorded in `bg-tasks/<slug>/runs.log` (newest first).
+  // The renderer turns each id into a full Run via the existing `runs:fetch`
+  // channel — bg-task transcripts now live at the global $WorkDir/runs/.
+  'bg-task:listRunIds': {
+    req: z.object({
+      slug: z.string(),
+      limit: z.number().int().positive().optional(),
+    }),
+    res: z.object({
+      runIds: z.array(z.string()),
+    }),
+  },
   // Embedded browser (WebContentsView) channels
   'browser:setBounds': {
     req: z.object({