feat(workspace): VS Code-style split panes, edge-to-edge session view

The console splits into up to four panes: a binary split tree of tmux
slots (client/src/lib/paneLayout.ts) drawn by PaneGrid.tsx, every pane an
absolutely placed sibling keyed by slot so splitting, swapping, resizing
or closing never remounts a live terminal. Ctrl/Cmd+click on a tab, a +
item or a sidebar session row opens it beside the focused pane (router
state, never the URL); a pane header drags onto another pane's edge to
split there or onto its middle to swap, picks another live session,
splits right/down (a not-shown session or a new terminal), or closes the
pane only. Dividers drag or take arrow keys. ?run= is the focused pane:
every layout change goes through change(), which pushes the URL with
focusOnly instead of an effect watching the focus (that ping-ponged with
open requests). The layout is kept per workspace in localStorage.

Only the focused pane's terminal takes the keyboard when it appears, and
the keyboard follows a focus change. A pane closes when its terminal
reports the exit; the run list prunes only a remembered layout on a
workspace's first read and a just-opened slot that never got listed, so
one empty read cannot wipe a split. A run ending on the home or a replay
closes its pane without leaving the page.

The session view now fills the page edge to edge: no page padding, the
tab bar and the right panel's activity bar one h-10 strip, and the tab
bar, pane headers and right panel on the sidebar/status bar colour
(surface-1) around terminals on the page colour.

client/src/i18n/locales/en/lanes.json

@@ -332,7 +332,7 @@
   "tree.newSession": "New session",
   "tree.noSessions": "No sessions yet",
   "tree.transcriptHint": "No live pane — opens its conversation; a message you send resumes it",
-  "tree.splitHint": "Live pane — Ctrl/Cmd+click opens it in a second pane",
+  "tree.splitHint": "Live pane — Ctrl/Cmd+click opens it in a split beside the focused pane",
   "tree.renameSession": "Rename session",
   "tree.archiveSession": "Archive — hide from this workspace (deletes nothing)",
   "tree.worktreeSession": "In its own worktree: .claude/worktrees/{{name}}",
@@ -391,5 +391,15 @@
   "tabs.terminal": "Terminal",
   "tabs.close": "Close tab (stops its session)",
   "tabs.full": "All 4 tabs are in use — close one first",
-  "tabs.agentSettings": "Agent settings…"
+  "tabs.agentSettings": "Agent settings…",
+  "tabs.splitHint": "Ctrl/Cmd+click: open in a split · drag onto a pane to place it",
+  "panes.drag": "Drag to move this pane — onto another pane's edge to split there, onto its middle to swap",
+  "panes.pick": "Show another session in this pane",
+  "panes.empty": "No session",
+  "panes.split.right": "Split right",
+  "panes.split.bottom": "Split down",
+  "panes.full": "4 panes is the most a workspace can show",
+  "panes.newTerminal": "New terminal",
+  "panes.close": "Close pane (its session keeps running as a tab)",
+  "panes.resize": "Resize panes"
 }

client/src/i18n/locales/vi/lanes.json

@@ -332,7 +332,7 @@
   "tree.newSession": "Session mới",
   "tree.noSessions": "Chưa có session",
   "tree.transcriptHint": "Không còn pane — mở hội thoại; gửi tin nhắn sẽ tiếp tục (resume) session",
-  "tree.splitHint": "Pane đang chạy — Ctrl/Cmd+click để mở ở pane thứ hai",
+  "tree.splitHint": "Pane đang chạy — Ctrl/Cmd+click để mở ở split cạnh pane đang focus",
   "tree.renameSession": "Đổi tên session",
   "tree.archiveSession": "Lưu trữ — ẩn khỏi workspace này (không xoá gì)",
   "tree.worktreeSession": "Trong worktree riêng: .claude/worktrees/{{name}}",
@@ -391,5 +391,15 @@
   "tabs.terminal": "Terminal",
   "tabs.close": "Đóng tab (dừng phiên của nó)",
   "tabs.full": "Đã dùng hết 4 tab — hãy đóng bớt một tab",
-  "tabs.agentSettings": "Cài đặt agent…"
+  "tabs.agentSettings": "Cài đặt agent…",
+  "tabs.splitHint": "Ctrl/Cmd+click: mở ở split · kéo thả vào một pane để đặt vị trí",
+  "panes.drag": "Kéo để di chuyển pane — thả vào cạnh pane khác để tách ở đó, vào giữa để đổi chỗ",
+  "panes.pick": "Hiện session khác trong pane này",
+  "panes.empty": "Không có session",
+  "panes.split.right": "Tách sang phải",
+  "panes.split.bottom": "Tách xuống dưới",
+  "panes.full": "Một workspace hiện tối đa 4 pane",
+  "panes.newTerminal": "Terminal mới",
+  "panes.close": "Đóng pane (session vẫn chạy dưới dạng tab)",
+  "panes.resize": "Đổi kích thước pane"
 }