[FEATURE] Visual UI for Agent Teams (and persistent always-on agents) in Claude Desktop

## Problem

Agent teams work well. In my test, two teammates cross-reviewed a script, withdrew 2 false positives, and downgraded 3 severities. But the only UI is the terminal agent panel: names plus a truncated spawn prompt. As a non-engineer I can't see who is on the team, what each teammate is doing, their progress, token cost, or the messages they exchange. Today the terminal view is readable mainly by the AI, not by the human who owns the work.

Community apps already show there's demand for this: **Munder Difflin** (a pixel-office GUI where each agent is a real `claude` CLI process) and **Hermes Agent**'s messaging-bot mode (agents living in Discord/Telegram/LINE).

## Request

1. **A team view in Claude Desktop**: member cards (role, status, current task), the shared task list as a board, the message flow between teammates, and per-teammate token/cost.
2. **Click a teammate to talk to them directly**, with the same UX as a normal session.
3. **An official option for persistent named agents**: long-lived teammates with their own identity and memory that can be reached from Desktop, mobile, or Channels (Discord/Telegram), with a cost guardrail such as an idle budget cap.

## Environment

- Claude Code v2.1.270
- WSL2 Ubuntu + tmux, Windows 11
- Claude Max
- `CLAUDE_CODE_EXPERIMENTAL_AGENT_TEAMS=1`

No files, tests, or implementation entry points are named. Start by separating the Desktop team view, direct teammate chat, and persistent-agent/channel requests into scoped proposals; done would require agreed acceptance criteria for member status, task and message visibility, cost reporting, persistence, and idle-budget behavior.

Written by the indexing model from the issue text.