feat(workspace): session view console as tabs, with New terminal

The 1/2/4 split view becomes a tab bar (ConsoleTabs.tsx): one tab per live
tmux slot (0-3) of the workspace, the active one being ?run=, every live tab's
pane kept mounted and hidden with CSS. The + menu opens a new tab in the first
free slot: New terminal (a plain shell - shell: true on POST
/api/lanes/:id/start, spawnShell, tool 'shell', no run_id/status change), any
installed enabled AI tool started bare, or Settings -> Agents. A tab's x stops
its session. splitViewStorage, &pane= and the sidebar's Ctrl/Cmd+click are gone.

server/lib/pty-run.js

@@ -22,9 +22,10 @@
  * Spawns `claude`, `codex` or `agy` (Antigravity) in the tmux pane based on
  * the tool parameter.
  *
- * A lane can hold up to four sessions, one per Workspace split pane: pane 0 is
- * `agenthub-lane-<laneId>` (the lane's own `run_id`), panes 1–3 are
- * `agenthub-lane-<laneId>-<slot>`.
+ * A lane can hold up to four sessions, one per Workspace tab: slot 0 is
+ * `agenthub-lane-<laneId>` (the lane's own `run_id`), slots 1–3 are
+ * `agenthub-lane-<laneId>-<slot>`. A slot holds an AI tool (`spawnRun`) or a
+ * plain shell (`spawnShell`, a Terminal tab).
  *
  * @author Nguyễn Ngọc Trí Vĩ <vinnt@smartgift.vn>
  */
@@ -498,6 +499,49 @@ function spawnRun(args) {
   return getRun(id);
 }
 
+/**
+ * A Workspace "Terminal" tab: the user's own default shell (tmux's, run with
+ * nothing after `--`) in a lane's pane slot. No AI tool, no prompt, nothing
+ * from the request but the slot — the cwd is the lane's. Recorded as tool
+ * `shell` so the tab can say what it is. The caller has already made sure the
+ * slot holds no live session.
+ */
+function spawnShell({ laneId, slot = 0, cwd }) {
+  if (!Number.isInteger(laneId)) throw makeErr("EBADLANE", "laneId must be an integer");
+  if (!Number.isInteger(slot) || slot < 0 || slot > MAX_PANE_SLOT) {
+    throw makeErr("EBADSLOT", `slot must be an integer 0–${MAX_PANE_SLOT}`);
+  }
+  if (!tmux.isTmuxAvailable()) throw makeErr("ETMUXMISSING", "tmux is not installed");
+  const id = runIdForLane(laneId, slot);
+  const env = {
+    AGENTHUB_LANE_ID: String(laneId),
+    AGENTHUB_RUN_ID: id,
+    ...(process.env.PATH ? { PATH: process.env.PATH } : {}),
+    ...desktopEnv(),
+  };
+  tmux.newSession({ name: id, cwd, argv: [], env });
+  dashboardRuns?.recordRun({
+    id,
+    sessionId: null,
+    mode: "interactive",
+    cwd,
+    tool: "shell",
+    model: null,
+    permissionMode: null,
+    effort: null,
+    resumeSessionId: null,
+    worktree: false,
+    router: null,
+    prompt: "",
+    status: "running",
+    startedAt: Date.now(),
+    endedAt: null,
+    exitCode: null,
+    laneId,
+  });
+  return getRun(id);
+}
+
 // Only a dashboard lane pane is a run. Without this, `DELETE /api/run/main`
 // would kill the user's own tmux session named `main`.
 function killRun(id) {
@@ -544,6 +588,7 @@ function listRuns() {
 
 module.exports = {
   spawnRun,
+  spawnShell,
   killRun,
   getRun,
   listRuns,