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.

server/lib/projects.js

@@ -0,0 +1,133 @@
+/**
+ * @file Projects: lanes grouped by the git repository they belong to, for the
+ * sidebar's project → workspace tree. A project is a repo's MAIN worktree root
+ * (the directory holding the common `.git`); a lane outside any repo lands in
+ * the `root: null` pseudo-project ("Folders"). Each project also lists the
+ * repo's worktrees from `git worktree list`, so a worktree no lane covers can
+ * be shown and adopted.
+ *
+ * Both reads shell out to git, so both are cached in memory: a cwd's root for
+ * the life of the process (a directory does not move between repos), a repo's
+ * worktree list for 30 s. `clearProjectCaches` (POST /api/projects/refresh)
+ * drops both. Which lane owns a worktree is recomputed on every call from the
+ * lane rows, so creating or removing a lane needs no invalidation. None of
+ * this runs on the polled `GET /api/lanes`.
+ * @author Nguyễn Ngọc Trí Vĩ <vinnt@smartgift.vn>
+ */
+
+const fs = require("node:fs");
+const path = require("node:path");
+const { git, listWorktrees, LANES_ROOT } = require("./worktree");
+
+const WORKTREE_TTL_MS = 30_000;
+const rootCache = new Map();
+const worktreeCache = new Map();
+
+function real(p) {
+  try {
+    return fs.realpathSync(p);
+  } catch {
+    return p;
+  }
+}
+
+function isUnder(p, dir) {
+  const rel = path.relative(dir, p);
+  return rel !== "" && !rel.startsWith("..") && !path.isAbsolute(rel);
+}
+
+/**
+ * The repository a directory belongs to: its main worktree's top level
+ * (realpath), or null when the directory is not inside a git repo.
+ * @param {string} cwd
+ * @returns {Promise<string|null>}
+ */
+async function projectRootFor(cwd) {
+  if (rootCache.has(cwd)) return rootCache.get(cwd);
+  let root = null;
+  try {
+    const { stdout } = await git(cwd, ["rev-parse", "--git-common-dir"]);
+    // Relative (".git") from the main worktree itself, absolute from a linked one.
+    const common = path.resolve(cwd, stdout.trim());
+    root = real(path.basename(common) === ".git" ? path.dirname(common) : common);
+  } catch {
+    root = null;
+  }
+  // A lane still being provisioned has no directory yet: ask again next time.
+  if (root || fs.existsSync(cwd)) rootCache.set(cwd, root);
+  return root;
+}
+
+async function worktreesFor(root) {
+  const hit = worktreeCache.get(root);
+  if (hit && Date.now() - hit.at < WORKTREE_TTL_MS) return hit.list;
+  let list = [];
+  try {
+    list = await listWorktrees(root);
+  } catch {
+    list = [];
+  }
+  worktreeCache.set(root, { at: Date.now(), list });
+  return list;
+}
+
+function clearProjectCaches() {
+  rootCache.clear();
+  worktreeCache.clear();
+}
+
+/**
+ * @param {{id:number, cwd:string}[]} lanes - lane rows, in id order
+ * @returns {Promise<object[]>} projects by name, the Folders pseudo-project last
+ */
+async function listProjects(lanes) {
+  const roots = await Promise.all(lanes.map((l) => projectRootFor(l.cwd)));
+  const byRoot = new Map();
+  lanes.forEach((lane, i) => {
+    const r = roots[i];
+    if (!byRoot.has(r)) byRoot.set(r, []);
+    byRoot.get(r).push(lane);
+  });
+  const lanesRoot = real(LANES_ROOT);
+  const projects = await Promise.all(
+    [...byRoot]
+      .filter(([root]) => root !== null)
+      .map(async ([root, own]) => {
+        const claudeDir = path.join(root, ".claude", "worktrees");
+        const worktrees = (await worktreesFor(root))
+          .map((w, i) => ({ ...w, path: real(w.path), main: i === 0 }))
+          // A worktree whose directory is gone (`prunable`) cannot be adopted.
+          .filter((w) => fs.existsSync(w.path))
+          .map((w) => ({
+            path: w.path,
+            branch: w.branch || null,
+            main: w.main,
+            workspace_id: own.find((l) => l.cwd === w.path)?.id ?? null,
+            ...(isUnder(w.path, claudeDir)
+              ? { source: "claude" }
+              : isUnder(w.path, lanesRoot)
+                ? { source: "agenthub" }
+                : {}),
+          }));
+        return {
+          root,
+          name: path.basename(root).replace(/\.git$/, "") || root,
+          workspaces: own.map((l) => l.id),
+          worktrees,
+        };
+      })
+  );
+  projects.sort((a, b) => a.name.localeCompare(b.name));
+  const folders = byRoot.get(null);
+  if (folders) {
+    projects.push({
+      root: null,
+      name: "Folders",
+      workspaces: folders.map((l) => l.id),
+      worktrees: [],
+    });
+  }
+  return projects;
+}
+
+module.exports = { projectRootFor, listProjects, clearProjectCaches };