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/client/runtime/tests/fake-api.ts

@@ -47,7 +47,7 @@ export class FakeApiClient implements IApiClient {
   onList: (payload: unknown) => Promise<RpcResponse<{ items: never[] }>> = () => Promise.resolve(ok({ items: [] }))
   onCreate: (payload: unknown) => Promise<RpcResponse<{ sessionId: SessionId }>> = () => Promise.resolve(ok({ sessionId: 'fk-new' as SessionId }))
   onHistory: (payload: { sessionId: SessionId; beforeSeq?: number; maxMessages?: number })
-  => Promise<RpcResponse<{ events: never[]; hasMore: boolean }>> =
+  => Promise<RpcResponse<{ events: never[]; hasMore: boolean; todos?: { content: string; status: 'pending' | 'in_progress' | 'completed' }[] }>> =
     () => Promise.resolve(ok({ events: [], hasMore: false }))
 
   onPrompt: (payload: unknown) => Promise<RpcResponse<{ accepted: true }>> = () => Promise.resolve(ok({ accepted: true as const }))