fix(studio): the travel panel builds its tiles with the book engine's factories

Figures, countries, maps and marks placed from the panel are the elements the
assistant adds, built by the shared factories; the panel keeps only their
placement. A trip map no longer carries the whole journey's trail, switching a
map's scope re-cuts it the way the engine does and clears the roads of the old
legs, and switching back to the whole journey restores the trail.

client/src/components/Studio/StudioShell.tsx

@@ -2,7 +2,7 @@ import { useEffect, useRef, useState } from 'react'
 import { createPortal } from 'react-dom'
 import { useNavigate } from 'react-router'
 import {
-  ArrowLeft, BookOpen, Check, ChevronDown, ClipboardPaste, Download, Maximize2, MessageSquare, Minus, Plus,
+  ArrowLeft, BookOpen, Check, ChevronDown, ClipboardPaste, Download, Maximize2, Minus, Plus,
   Redo2, Sparkles, Undo2,
 } from 'lucide-react'
 import { useJourneyStudio } from '../../pages/journeyStudio/useJourneyStudio'
@@ -21,7 +21,7 @@ import { PeerBadges } from './PeerBadges'
 import { TrimField } from './TrimField'
 import { Tooltip } from '../shared/Tooltip'
 import { useStudioStore } from '../../store/studioStore'
-import StudioAssistantPanel, { StudioPageStage } from './StudioAssistantPanel'
+import { StudioAssistantColumn, StudioAssistantToggle, StudioPageStage } from './StudioAssistantPanel'
 import { useStudioAssistant, type StudioAssistant } from './useStudioAssistant'
 import '../../styles/dashboard.css'
 import '../../styles/studio.css'
@@ -128,12 +128,13 @@ export default function StudioShell() {
             spreadIndex={s.activeSpread}
             page={s.page}
             stats={s.stats}
+            path={s.path}
             source={s.source}
             setPageNumbers={s.setPageNumbers}
             t={s.t}
             locale={s.locale}
           />
-          <AssistantColumn s={s} assistant={assistant} />
+          <StudioAssistantColumn assistant={assistant} title={s.journey?.title} />
         </div>
         <StudioPageStage assistant={assistant} />
 
@@ -153,12 +154,6 @@ export default function StudioShell() {
 
 type Studio = ReturnType<typeof useJourneyStudio>
 
-/** The chat column at the end of the body, while it is open. */
-function AssistantColumn({ s, assistant }: { s: Studio; assistant: StudioAssistant }) {
-  if (!assistant.open) return null
-  return <StudioAssistantPanel assistant={assistant} title={s.journey?.title || s.t('journey.title')} />
-}
-
 function StudioBar({
   s, bookView, setBookView, onExport, assistant,
 }: {
@@ -238,17 +233,7 @@ function StudioBar({
 
         <AutoLayoutButton s={s} />
         {/* The book's assistant, as a column beside the page; only where it can run for this user. */}
-        {assistant.available && (
-          <button type="button"
-            className={`st-tool ${assistant.open ? 'is-on' : ''}`}
-            onClick={assistant.toggle}
-            aria-pressed={assistant.open}
-            title={s.t('journey.studio.assistant.toggleHint')}
-          >
-            <MessageSquare size={14} />
-            <span className="st-tool-label">{s.t('journey.studio.assistant.toggle')}</span>
-          </button>
-        )}
+        <StudioAssistantToggle assistant={assistant} />
         <button type="button"
           className="st-tool is-primary"
           onClick={onExport}