feat(web): list background tasks in the session header

The task registry has run every background bash, pwsh, pty-send, and
one-shot subagent since it landed, but only the model could read it: a
human at the Web client could not see that a build was running, tell a
finished task from a stuck one, or find its outcome anywhere but the
`run_in_background` tool card that printed an id and never updated.

Task state now reaches the browser as one whole-snapshot `session/tasks`
mux frame per session, pushed at every registry commit that changes what
that session can see. `TaskService` gains `onTasksChanged`, which is
owner-granular because owner-disposal removal is a change no per-task
record can express. The carrier reads the exact owner the listener hands
it, so a push stays correct while that scope tears down, and reads the
baseline through the non-resuming `ctx.agents.get` so listing never
revives a cold session. The client keeps a last-wins mirror on
`SessionListState`, and a new `dsh-client-ui-task` package renders it
beside the subagent catalog — rendering nothing at all until the session
has a task, so an ordinary conversation grows no new chrome.

Streamed per-task output and human-initiated cancellation are separate
phases; the note records why neither has to undo this channel, and why
no Web path may call the consuming `ctx.tasks.read()`.

packages/host/apiproxy/src/api/events.schema.ts

@@ -13,6 +13,7 @@ import { approvalRequestIdSchema } from './approvals.schema.ts'
 import {
   contentBlockSchema, messageIdSchema, sessionEventSchema, sessionIdSchema, toolEventViewSchema,
 } from './sessions.schema.ts'
+import { taskViewSchema } from './tasks.schema.ts'
 import { workspaceIdSchema, workspaceViewSchema } from './workspace.schema.ts'
 
 /** Question shape validated strictly against core dsh-user-interaction. */
@@ -58,6 +59,7 @@ export const muxFrameSchema = z.discriminatedUnion('type', [
       message: messageSchema,
     })),
   }),
+  z.object({ type: z.literal('session/tasks'), sessionId: sessionIdSchema, tasks: z.array(taskViewSchema) }),
   // value stays wide: it already passed its unit's own schema on the host,
   // and deep-validating here would import every domain's schema into the carrier.
   z.object({ type: z.literal('session/projection'), sessionId: sessionIdSchema, key: z.string().min(1), value: z.unknown(), seq: z.number().int().nonnegative() }),