Add cmux support to teammateMode

Feature request

Currently teammateMode in settings.json only supports tmux, in-process, and auto (which falls back to in-process when not in a tmux session). It would be useful to add cmux as an additional backend so users running cmux can get the same split-pane experience tmux users get.

Current behavior

• In a tmux session: teammates spawn in tmux split panes (great UX)
• In cmux (or any non-tmux multiplexer): falls back to in-process, no split-pane UI

Proposed behavior

• Add "cmux" as a valid teammateMode enum value
• Have auto detect cmux sessions and use cmux split panes when available
• Document the cmux integration alongside tmux/iTerm2

Why

Users who prefer cmux over tmux currently have to either switch multiplexers or lose the split-pane teammate UX. Adding cmux as a first-class backend removes that friction.

Environment

• macOS (Darwin 25.4.0)
• Claude Code (current version)