feat: re-introduce split-pane TUI as a polished feature

[ronishrohan]

Background

The /split beta feature was removed in commit 8d917ba because the TUI had several layout issues:

• Streaming content appeared underneath the input area during active streaming
• Subagents UI was misaligned in split mode
• Typing / in split mode broke the layout further
• Theme picker and other popups were transparent/overlapping in split mode
• All menus/popups behaved incorrectly in split mode

What to re-implement

• /split command to open two side-by-side chat panes
• Ctrl+K to toggle focus between panes
• /split left, /split right, /split close
• Proper popup/overlay rendering that doesn't break in split layout
• Auto-scroll that works correctly in both panes
• Fix streaming content placement (should appear above input, not below)

Key files to restore/rework

• src/ui/ink-terminal.tsx — SplitChatView, SplitPaneView, SplitPaneSummary, setSplitPane, clearViewport
• src/interactive-session-controller.ts — handleSplitCommand, focusSplitSide, closeSplit, syncSplitPane
• src/task-ui-bridge.ts — onRuntimeUpdate for cross-pane UI sync
• src/ui/components/prompt-input.tsx — onSplitToggle, Ctrl+K binding
• src/commands.ts — /split command definition

Design notes

• Fix all menu/popup layering issues before shipping (no transparent backgrounds, no overlap with content)
• Fix autoscroll on new messages to work like industry-standard CLIs
• Ensure streaming content renders above the input area during active turns
• Add a visible [beta] label in the UI when split is active