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/beads/beads.go

@@ -357,6 +357,13 @@ func (b *Beads) run(args ...string) ([]byte, error) {
 	return stdout.Bytes(), nil
 }
 
+// Run executes a bd command and returns stdout.
+// This is a public wrapper around the internal run method for cases where
+// callers need to run arbitrary bd commands.
+func (b *Beads) Run(args ...string) ([]byte, error) {
+	return b.run(args...)
+}
+
 // wrapError wraps bd errors with context.
 func (b *Beads) wrapError(err error, stderr string, args []string) error {
 	stderr = strings.TrimSpace(stderr)
@@ -1144,6 +1151,38 @@ func (b *Beads) UpdateAgentState(id string, state string, hookBead *string) erro
 	return nil
 }
 
+// SetHookBead sets the hook_bead slot on an agent bead.
+// This is a convenience wrapper that only sets the hook without changing agent_state.
+// Per gt-zecmc: agent_state ("running", "dead", "idle") is observable from tmux
+// and should not be recorded in beads ("discover, don't track" principle).
+func (b *Beads) SetHookBead(agentBeadID, hookBeadID string) error {
+	// Set the hook using bd slot set
+	// This updates the hook_bead column directly in SQLite
+	_, err := b.run("slot", "set", agentBeadID, "hook", hookBeadID)
+	if err != nil {
+		// If slot is already occupied, clear it first then retry
+		errStr := err.Error()
+		if strings.Contains(errStr, "already occupied") {
+			_, _ = b.run("slot", "clear", agentBeadID, "hook")
+			_, err = b.run("slot", "set", agentBeadID, "hook", hookBeadID)
+		}
+		if err != nil {
+			return fmt.Errorf("setting hook: %w", err)
+		}
+	}
+	return nil
+}
+
+// ClearHookBead clears the hook_bead slot on an agent bead.
+// Used when work is complete or unslung.
+func (b *Beads) ClearHookBead(agentBeadID string) error {
+	_, err := b.run("slot", "clear", agentBeadID, "hook")
+	if err != nil {
+		return fmt.Errorf("clearing hook: %w", err)
+	}
+	return nil
+}
+
 // UpdateAgentCleanupStatus updates the cleanup_status field in an agent bead.
 // This is called by the polecat to self-report its git state (ZFC compliance).
 // Valid statuses: clean, has_uncommitted, has_stash, has_unpushed