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()`.

docs/core-data-structures/tasks.md

@@ -151,4 +151,4 @@ interface TaskRead {
 
 ## Service behavior
 
-The abstract [`TaskService`](../../packages/tasks/tasks/src/index.ts) seam defines atomic `start`, caller-scoped `get` and `list`, `read`, `kill`, bounded `wait`, contained `onTaskDone` listeners, and the `attachSurface` availability fence; [`LocalTaskService`](../../packages/tasks/tasks-local/src/index.ts) is the process-local implementation. Authorization compares owner sessions; owner cleanup selects the exact registered `Agent` instance. See [`dsh-tasks`](../../packages/tasks/tasks/README.md) for the seam contract, [`dsh-tasks-local`](../../packages/tasks/tasks-local/README.md) for the registry lifecycle, and [`dsh-tool-tasks`](../../packages/tasks/tool-tasks/README.md) for the model-facing surface.
+The abstract [`TaskService`](../../packages/tasks/tasks/src/index.ts) seam defines atomic `start`, caller-scoped `get` and `list`, `read`, `kill`, bounded `wait`, contained `onTaskDone` and `onTasksChanged` listeners, and the `attachSurface` availability fence; [`LocalTaskService`](../../packages/tasks/tasks-local/src/index.ts) is the process-local implementation. The two listener kinds are not nested: `onTaskDone` delivers one terminal record under first-wins semantics a control surface couples to notice delivery, while `onTasksChanged` observes every visible-set change — registration, the stopping transition, settlement, and owner-disposal removal — carrying only the owner whose set moved, or `undefined` when an unowned task changed and every caller's set moved with it. Authorization compares owner sessions; owner cleanup selects the exact registered `Agent` instance. See [`dsh-tasks`](../../packages/tasks/tasks/README.md) for the seam contract, [`dsh-tasks-local`](../../packages/tasks/tasks-local/README.md) for the registry lifecycle, and [`dsh-tool-tasks`](../../packages/tasks/tool-tasks/README.md) for the model-facing surface.