fix: remove observable states from agent_state (discover, don't track)

The agent_state field was recording observable state like "running",
"dead", "idle" which violated the "Discover, Don't Track" principle.
This caused stale state bugs where agents were marked "dead" in beads
but actually running in tmux.

Changes:
- Remove daemon's checkStaleAgents() which marked agents "dead"
- Simplify ensureXxxRunning() to use tmux.IsClaudeRunning() directly
- Remove reportAgentState() calls from gt prime and gt handoff
- Add SetHookBead/ClearHookBead helpers that don't update agent_state
- Use ClearHookBead in gt done and gt unsling
- Simplify gt status to derive state from tmux, not bead

Non-observable states (stuck, awaiting-gate, muted, paused) are still
set because they represent intentional agent decisions that can't be
discovered from tmux state.

Fixes: gt-zecmc

🤖 Generated with [Claude Code](https://claude.com/claude-code)

Co-Authored-By: Claude Opus 4.5 <noreply@anthropic.com>

internal/cmd/sling.go

@@ -1033,13 +1033,13 @@ func updateAgentHookBead(agentID, beadID, workDir, townBeadsDir string) {
 	}
 
 	// Run from workDir WITHOUT BEADS_DIR to enable redirect-based routing.
-	// Update agent_state to "running" and set hook_bead to the slung work.
-	// For same-database beads, the hook slot is set via `bd slot set`.
+	// Set hook_bead to the slung work (gt-zecmc: removed agent_state update).
+	// Agent liveness is observable from tmux - no need to record it in bead.
 	// For cross-database scenarios, slot set may fail gracefully (warning only).
 	bd := beads.New(bdWorkDir)
-	if err := bd.UpdateAgentState(agentBeadID, "running", &beadID); err != nil {
+	if err := bd.SetHookBead(agentBeadID, beadID); err != nil {
 		// Log warning instead of silent ignore - helps debug cross-beads issues
-		fmt.Fprintf(os.Stderr, "Warning: couldn't update agent %s state: %v\n", agentBeadID, err)
+		fmt.Fprintf(os.Stderr, "Warning: couldn't set agent %s hook: %v\n", agentBeadID, err)
 		return
 	}
 }