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/client/ui-workspace/tests/tree.spec.ts

@@ -17,7 +17,7 @@ const list = (...items: SessionSummary[]): SessionListState => ({
   ids: items.map(item => item.id),
   byId: Object.fromEntries(items.map(item => [item.id, item])),
   current: undefined,
-  phase: 'ready', subagentsByParent: {}, currentAddress: undefined,
+  phase: 'ready', subagentsByParent: {}, tasksBySession: {}, currentAddress: undefined,
 })
 const workspace = (id: string, sessionIds: string[], title = id): WorkspaceView => ({
   workspaceId: wid(id), path: `/projects/${id}`, title,

packages/client/ui-workspace/tests/workspace-browser.spec.tsx

@@ -29,7 +29,7 @@ const sessionState = (items: readonly SessionSummary[], overrides: Partial<Sessi
   byId: Object.fromEntries(items.map(item => [item.id, item])),
   current: undefined,
   phase: 'ready',
-  subagentsByParent: {},
+  subagentsByParent: {}, tasksBySession: {},
   currentAddress: undefined,
   ...overrides,
 })

packages/client/ui-workspace/tests/workspace-picker.spec.tsx

@@ -28,7 +28,7 @@ function hook<T>(snapshot: T) {
   return function select<S>(selector: (state: T) => S): S { return selector(snapshot) }
 }
 const sessions: SessionListState = {
-  ids: [], byId: {}, current: undefined, phase: 'ready', subagentsByParent: {}, currentAddress: undefined,
+  ids: [], byId: {}, current: undefined, phase: 'ready', subagentsByParent: {}, tasksBySession: {}, currentAddress: undefined,
 }
 const workspaceState = (items: readonly WorkspaceView[]): WorkspaceListState => ({
   items, archivedSessionIds: [], state: 'idle', phase: 'ready', error: null, baselinesReady: true,