fix(gui): tail history page carries the full-log todo projection

The client's todos projection derived only from the paged display window,
so reopening a session whose last todo/write preceded the tail page showed
an empty plan until the user paged back — session-level state cannot be
reconstructed from an arbitrary window. The host owns the full log, so the
tail history response now attaches todos (latest todo/write backscan, the
same posture as the view pairing); installWindow seeds it, window rebuilds
preserve it, and any in-window or live write keeps overwriting it. The
fixture mirrors the host; docs and both Agent Notes record the mechanism.

packages/host/apiproxy/src/api/sessions.ts

@@ -5,7 +5,7 @@
  */
 
 import type { ContentBlock } from '@deepseek-ai/dsh-llm/types'
-import type { SessionEvent, SessionId } from '@deepseek-ai/dsh-session/types'
+import type { SessionEvent, SessionId, TodoItem } from '@deepseek-ai/dsh-session/types'
 import type { RpcId, RpcRequest, RpcResponse } from './rpc.ts'
 import type { ToolEventView } from './events.ts'
 
@@ -60,9 +60,13 @@ export interface SessionsApi {
    * Each entry pairs the raw SessionEvent with the host-computed view (tool events whose
    * presenter produced one, evaluated against the registry at pagination time); the client
    * rebuilds the surface from the events with the shared fold.
+   * The tail page (beforeSeq absent) also carries `todos` — the session's current todo
+   * projection (latest `todo/write` over the FULL log, independent of the page window) —
+   * so a paged client restores the plan without walking history; absent when the session
+   * never wrote one. Older pages omit it (the projection is session-level, not per-page).
    */
   history(request: RpcRequest<{ sessionId: SessionId; beforeSeq?: number; maxMessages?: number }>):
-  Promise<RpcResponse<{ events: HistoryEntry[]; hasMore: boolean }>>
+  Promise<RpcResponse<{ events: HistoryEntry[]; hasMore: boolean; todos?: TodoItem[] }>>
 
   /** Sends a message. content is core's ContentBlock[] verbatim; mode maps 1:1 — queue→send, steer→steer. */
   prompt(request: RpcRequest<{ sessionId: SessionId; mode: 'queue' | 'steer'; content: ContentBlock[] }>):