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/connection/src/client/api.ts

@@ -17,6 +17,7 @@ export type {
   SettingsApi, SettingsNamespaceView, SettingsPathOpView, SettingsSecretView,
   CredentialsApi, CredentialView, ConfigurableProviderView, DiscoveredModelView, LlmApi,
   SubagentsApi, SubagentAddress, SubagentCatalog, SubagentListEntry, SubagentPromptReceipt,
+  TaskView,
 } from '@deepseek-ai/dsh-host-apiproxy/api'
 export type { ToolCallView, ToolResultView } from '@deepseek-ai/dsh-tools/presentation'
 export type {

packages/client/connection/src/client/index.ts

@@ -22,6 +22,7 @@ export type {
   ModelCatalogFailure, ModelCatalogModel, ModelProviderGroup, ModelReasoning,
   MessageId, ModelReasoningEffort, ModelTarget, QueueAction, QueuedInboxItem, SessionModels,
   SubagentsApi, SubagentAddress, SubagentCatalog, SubagentListEntry, SubagentPromptReceipt,
+  TaskView,
   RpcRequest, RpcResponse, RpcResult, RpcError, RpcErrorCode,
   ClientRequest, ServerResponse, ServerRequest, ClientResponse, RpcMessage, RpcReceipt,
   IApiClient, SessionId, SessionEvent, ContentBlock, StreamChunk,