chore(tui): remove dead branch cleanup code

- drop unused TUI helpers, test-only layout scaffolding, and stale public debug exports
- remove an unused profiler import and trim test-only coverage for deleted helpers

ui-tui/src/app/turnStore.ts

@@ -1,7 +1,7 @@
 import { atom } from 'nanostores'
 import { useSyncExternalStore } from 'react'
 
-import { appendToolShelfMessage, isTodoDone } from '../lib/liveProgress.js'
+import { isTodoDone } from '../lib/liveProgress.js'
 import type { ActiveTool, ActivityItem, Msg, SubagentProgress, TodoItem } from '../types.js'
 
 const buildTurnState = (): TurnState => ({
@@ -64,9 +64,6 @@ export const archiveTodosAtTurnEnd = () => {
   return [msg]
 }
 
-export const appendTurnSegment = (msg: Msg) =>
-  patchTurnState(state => ({ ...state, streamSegments: appendToolShelfMessage(state.streamSegments, msg) }))
-
 export const resetTurnState = () => $turnState.set(buildTurnState())
 
 export interface TurnState {