feat(tmux): add shared muse tmux socket manager with CLI and agent [TOOL tmux.*] integration

docs/AGENT-TOOLING.md

@@ -72,7 +72,38 @@ box muse <self> send --thread <thread_uuid> "<message>"
 
 ---
 
-## 4. Best Practices & Invariants
+## 4. Shared Tmux Socket Tooling (`muse tmux` & `[TOOL tmux.*]`)
+
+Agents and operators can spawn background sessions and send keystrokes to long-running tasks via the shared socket `/tmp/tmux-muse.sock`.
+
+### Via Native CLI:
+```bash
+# List sessions on shared socket
+muse <account> tmux list
+
+# Create or send commands to a background session
+muse <account> tmux send <session> "command to execute"
+
+# Capture recent scrollback output from a session
+muse <account> tmux capture <session> --lines 30
+
+# Kill a session
+muse <account> tmux kill <session>
+```
+
+### Via Autonomous Agent Directives:
+Agents can emit structured tool calls in sidechats:
+```text
+[TOOL tmux.new {"session": "build-worker", "command": "python3 /srv/worker.py"}]
+[TOOL tmux.send {"session": "build-worker", "keys": "ls -la"}]
+[TOOL tmux.capture {"session": "build-worker", "lines": 20}]
+[TOOL tmux.list {}]
+[TOOL tmux.kill {"session": "build-worker"}]
+```
+
+---
+
+## 5. Best Practices & Invariants
 
 1. **Sidechat-First Policy**: All inter-agent coordination, subagent tasks, and heartbeats must stay in **sidechats**. Do not send automated routine messages to `main` chat.
 2. **Sub-Agent Prioritization**: Break down complex diagnostic or verification jobs by delegating sub-tasks to dedicated subagent threads.