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/src/lib/api.ts

@@ -404,6 +404,7 @@ import type {
   LaneFileContent,
   LaneTreeEntry,
   LaneCounts,
+  Project,
   LaneGitFacts,
   LaneRuntime,
   LaneTool,
@@ -2416,6 +2417,14 @@ export const api = {
       }>("/remote-sources/sync-all", { method: "POST" }),
   },
 
+  /** Lanes grouped by git repo, with each repo's worktrees (server/lib/projects.js). */
+  projects: {
+    /** GET /api/projects — read on demand by the sidebar tree, never polled. */
+    list: () => request<{ projects: Project[] }>("/projects"),
+    /** POST /api/projects/refresh — drop the cached roots/worktree lists, then list. */
+    refresh: () => request<{ projects: Project[] }>("/projects/refresh", { method: "POST" }),
+  },
+
   // ──────────────────────────────── Lanes API ────────────────────────────────
   /** Agent work lanes: durable units of parallel work, one cwd per lane.
    *  Maps to `server/routes/lanes.js`. */