feat(desktop): workspace bar carries the full path as the breadcrumb

The chat header is display:none inside the pane tree (title lives in the
zone tab), so the header cwd segment never shows in the main layout.
Append displayPath(cwd) to the always-visible workspace strip instead.

Co-Authored-By: Claude Opus 4.7 <noreply@anthropic.com>

apps/desktop/src/app/chat/workspace-bar.tsx

@@ -3,7 +3,7 @@ import { useStore } from '@nanostores/react'
 import { pickAndChangeWorkspace } from '@/app/shell/workspace-menu'
 import { Button } from '@/components/ui/button'
 import { useI18n } from '@/i18n'
-import { pathLeaf } from '@/lib/display-path'
+import { displayPath, pathLeaf } from '@/lib/display-path'
 import { FolderOpen } from '@/lib/icons'
 import { $projectTree, projectNameForCwd } from '@/store/projects'
 import { $currentBranch } from '@/store/session'
@@ -26,6 +26,15 @@ export function WorkspaceBar({ cwd, onChangeWorkspace }: { cwd: string; onChange
       <span className="min-w-0 flex-1 truncate">
         {trimmed ? name : copy.chooseWorkspace}
         {trimmed && branch ? <span className="text-muted-foreground/60"> · {branch}</span> : null}
+        {/* Breadcrumb trail: the chat header (which would carry this) is hidden
+            inside the pane tree — the title lives in the zone tab — so the
+            full workspace path rides here where it stays visible. */}
+        {trimmed ? (
+          <span className="text-muted-foreground/50" title={trimmed}>
+            {' '}
+            · {displayPath(trimmed)}
+          </span>
+        ) : null}
       </span>
       <Button
         className="h-5 px-1.5 text-xs text-muted-foreground"