Add configurable tmux split direction for agent team panes

Feature Request

When using agent teams with teammateMode: "tmux", teammate panes are spawned below the main pane. It would be useful to have a configuration option to control the split direction, so teammates can be spawned to the right instead.

Motivation

On wide monitors or ultrawide setups, horizontal (right-side) splits make much better use of screen real estate than vertical (below) splits. The main pane where you interact with Claude benefits from having full width, and teammate status is easier to monitor side-by-side.

Proposed Solution

Add a setting like teammateSplitDirection in ~/.claude/settings.json:

{
  "teammateSplitDirection": "horizontal"
}

Where:

• "vertical" (default, current behavior) — splits below
• "horizontal" — splits to the right

Related Issues

• #23615 — Agent teams should spawn in new tmux window, not split current pane
• #23574 — Add WezTerm as a split-pane backend for agent teams