feat(ui): sidebar project tree, status bar and a tabbed workbench for workspaces

The Workspace page's lane strip moves into the sidebar as a project tree:
workspaces grouped by git repository (new GET /api/projects, cached in
memory, POST /api/projects/refresh), untracked worktrees with Adopt, inline
rename, drag/Alt+arrow ordering and a right-click row menu. The selected
workspace is the URL's ?lane=, one shared lane list feeds the tree, the new
bottom status bar and the page. The Changes panel gains an activity bar
(Files / Changes / Sessions, with resume), and split panes get a header.

client/README.md

@@ -184,6 +184,8 @@ client/
 │   │   ├── EventDetail.tsx  # Inline hook payload viewer (used by ActivityFeed + SessionDetail)
 │   │   ├── EmptyState.tsx
 │   │   ├── Sidebar.tsx
+│   │   ├── ProjectTree.tsx  # Sidebar Projects section: workspaces grouped by repo (`GET /api/projects`), untracked worktrees + Adopt, row menu
+│   │   ├── StatusBar.tsx    # Fixed bottom bar: Live/Disconnected, version, running / needs-you counts, today's cost
 │   │   ├── Layout.tsx
 │   │   ├── RemoteSources.tsx  # Remote Data Sources settings panel (SSH multi-machine collection)
 │   │   ├── SessionToolBadge.tsx  # The CLI that produced a non-Claude session, by its AI Tools label (nothing for Claude)
@@ -217,6 +219,7 @@ client/
 │   │
 │   ├── hooks/
 │   │   ├── useWebSocket.ts      # Auto-reconnecting WebSocket hook
+│   │   ├── useLanes.ts          # ONE shared lane list (GET /api/lanes + `lane_update` frames, refetch on reconnect) for the sidebar tree, status bar and Workspace page
 │   │   ├── useNotifications.ts  # Browser push notification triggers
 │   │   └── useTheme.ts          # Dark/light/system mode + per-mode named theme: `dark` class, `data-mode`, `data-theme` on <html>, persisted to localStorage
 │   │
@@ -469,7 +472,7 @@ graph TB
     CcConfig["/cc-config (redirect)"]
     Lanes["/lanes (redirect)"]
     Run["/run (redirect)"]
-    Workspace["/workspace"]
+    Workspace["/workspace?lane=<id>"]
     Settings["/settings (tabs: dashboard | claude-code | ...)"]
     NF["/* (NotFound)"]