feat: group chat sidebar by project folder with collapsible sections

Restructure the chat list panel to group sessions by working directory
(project folder), similar to Codex App. Each project folder is shown as
a collapsible section with a folder icon and project name. Features:

- Sessions grouped by working_directory, sorted by most recent activity
- Collapsible folder sections with persistent state in localStorage
- Per-folder "+" button to create new chat in that project
- "Open project folder" button in sidebar header with FolderPicker dialog
- NavRail new-chat button creates sessions in most recent project
- Chat header shows "projectName / sessionTitle" breadcrumb
- Search filters both folder names and session titles

Co-Authored-By: Claude Opus 4.6 <noreply@anthropic.com>

Author: 7418

src/app/chat/[id]/page.tsx

@@ -21,6 +21,7 @@ export default function ChatSessionPage({ params }: ChatSessionPageProps) {
   const [sessionTitle, setSessionTitle] = useState<string>('');
   const [sessionModel, setSessionModel] = useState<string>('');
   const [sessionMode, setSessionMode] = useState<string>('');
+  const [projectName, setProjectName] = useState<string>('');
   const { setWorkingDirectory, setSessionId, setSessionTitle: setPanelSessionTitle, setPanelOpen } = usePanel();
 
   // Load session info and set working directory
@@ -32,6 +33,7 @@ export default function ChatSessionPage({ params }: ChatSessionPageProps) {
           const data: { session: ChatSession } = await res.json();
           if (data.session.working_directory) {
             setWorkingDirectory(data.session.working_directory);
+            localStorage.setItem("codepilot:last-working-directory", data.session.working_directory);
           }
           setSessionId(id);
           setPanelOpen(true);
@@ -40,6 +42,7 @@ export default function ChatSessionPage({ params }: ChatSessionPageProps) {
           setPanelSessionTitle(title);
           setSessionModel(data.session.model || '');
           setSessionMode(data.session.mode || 'code');
+          setProjectName(data.session.project_name || '');
         }
       } catch {
         // Session info load failed - panel will still work without directory
@@ -112,9 +115,15 @@ export default function ChatSessionPage({ params }: ChatSessionPageProps) {
       {/* Chat title bar */}
       {sessionTitle && (
         <div
-          className="flex items-center justify-center px-4 py-2"
+          className="flex items-center justify-center px-4 py-2 gap-1"
           style={{ WebkitAppRegion: 'drag' } as React.CSSProperties}
         >
+          {projectName && (
+            <>
+              <span className="text-xs text-muted-foreground shrink-0">{projectName}</span>
+              <span className="text-xs text-muted-foreground shrink-0">/</span>
+            </>
+          )}
           <h2 className="text-sm font-medium text-foreground/80 truncate max-w-md">
             {sessionTitle}
           </h2>