[FEATURE] Add WezTerm as a split-pane backend for agent teams (teammateMode)

Preflight Checklist

• [x] I have searched existing requests and this feature hasn't been requested yet
• [x] This is a single feature request (not multiple features)

Problem Statement

WezTerm users cannot use split-pane mode for agent teams. The current teammateMode: "tmux" setting only supports tmux and iTerm2 as backends. WezTerm is a popular GPU-accelerated, cross-platform terminal emulator with a full CLI for programmatic pane management — making it a natural fit as a third split-pane backend.

Currently, WezTerm users are forced to either:

1. Run tmux inside WezTerm (redundant — WezTerm is already a multiplexer)
2. Use in-process mode (no visual split panes)

Proposed Solution

Add a WezTerm backend for teammateMode that uses WezTerm's CLI to spawn teammates in native split panes.

WezTerm's CLI provides direct equivalents to every tmux command Claude Code needs:

| Operation | tmux | WezTerm CLI |
|-----------|------|-------------|
| Split horizontally | tmux split-window -h -- cmd | wezterm cli split-pane --right -- cmd |
| Split vertically | tmux split-window -v -- cmd | wezterm cli split-pane --bottom -- cmd |
| List panes | tmux list-panes | wezterm cli list |
| Focus a pane | tmux select-pane -t N | wezterm cli activate-pane --pane-id N |
| Get pane info | tmux display -p '#{pane_id}' | WEZTERM_PANE env var (auto-set per pane) |
| Top-level split | N/A | wezterm cli split-pane --top-level --bottom -- cmd |

Detection is straightforward — WezTerm sets TERM_PROGRAM=WezTerm in the environment.

Key implementation detail: wezterm cli split-pane returns the new pane ID on success, and each spawned pane automatically receives a WEZTERM_PANE environment variable. This makes tracking and targeting teammate panes trivial.

Suggested behavior:

• When teammateMode is "tmux" or "auto", check for TERM_PROGRAM=WezTerm alongside existing tmux/iTerm2 detection
• Or add "wezterm" as an explicit teammateMode value

Alternative Solutions

• Running tmux inside WezTerm works but is redundant since WezTerm is itself a multiplexer with full pane management
• In-process mode works but lacks the visual benefit of seeing all teammates simultaneously

Priority

Medium - Significant impact on productivity

Feature Category

CLI commands and flags

Use Case Example

# WezTerm CLI pane management works out of the box:
$ wezterm cli split-pane --right -- echo "hello from new pane"
3    # returns new pane ID

$ wezterm cli split-pane --bottom -- bash -l
5    # returns new pane ID

$ wezterm cli list
WINID TABID PANEID WORKSPACE SIZE   TITLE      CWD
0     0     0      default   120x40 zsh        /Users/me
0     0     3      default   60x40  zsh        /Users/me
0     0     5      default   120x20 zsh        /Users/me

$ wezterm cli activate-pane --pane-id 3
# focuses the specified pane

Agent teams would use this the same way they use tmux:

# Claude Code spawns teammates in native WezTerm panes:
wezterm cli split-pane --right -- claude --resume <session-id> --teammate
wezterm cli split-pane --bottom -- claude --resume <session-id> --teammate

Additional Context

Environment:

• Claude Code version: 2.1.33
• OS: macOS Darwin 25.3.0 (arm64)
• Terminal: WezTerm 20240203-110809-5046fc22
• TERM_PROGRAM=WezTerm is set automatically

References:

• WezTerm CLI split-pane docs: https://wezfurlong.org/wezterm/cli/cli/split-pane.html
• WezTerm CLI list docs: https://wezfurlong.org/wezterm/cli/cli/list.html
• Related: #19555 (built-in multiplexer vision), #23572 (tmux/iTerm2 silent fallback bug)
• WezTerm is written in Rust, GPU-accelerated, supports macOS/Linux/Windows
• WezTerm has a growing user base and is commonly used by developers who prefer it over iTerm2