Unify agent startup with Manager pattern

Refactors all agent startup paths (witness, refinery, crew, polecat) to use
a consistent Manager interface with Start(), Stop(), IsRunning(), and
SessionName() methods.

Includes:
- Witness manager with GUPP propulsion nudge for startup
- Refinery manager for engineer sessions
- Crew manager for worker agents
- Session/polecat manager updates
- claude_settings_check doctor check for settings validation
- Settings management consolidated from rig/manager.go
- Settings location moved outside source repos to prevent conflicts

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

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

internal/rig/manager.go

@@ -12,6 +12,7 @@ import (
 	"time"
 
 	"github.com/steveyegge/gastown/internal/beads"
+	"github.com/steveyegge/gastown/internal/claude"
 	"github.com/steveyegge/gastown/internal/config"
 	"github.com/steveyegge/gastown/internal/git"
 	"github.com/steveyegge/gastown/internal/templates"
@@ -436,6 +437,33 @@ Use crew for your own workspace. Polecats are for batch work dispatch.
 		return nil, fmt.Errorf("creating polecats dir: %w", err)
 	}
 
+	// Install Claude settings for all agent directories.
+	// Settings are placed in parent directories (not inside git repos) so Claude
+	// finds them via directory traversal without polluting source repos.
+	fmt.Printf("  Installing Claude settings...\n")
+	settingsRoles := []struct {
+		dir  string
+		role string
+	}{
+		{witnessPath, "witness"},
+		{filepath.Join(rigPath, "refinery"), "refinery"},
+		{crewPath, "crew"},
+		{polecatsPath, "polecat"},
+	}
+	for _, sr := range settingsRoles {
+		if err := claude.EnsureSettingsForRole(sr.dir, sr.role); err != nil {
+			fmt.Fprintf(os.Stderr, "  Warning: Could not create %s settings: %v\n", sr.role, err)
+		}
+	}
+	fmt.Printf("   ✓ Installed Claude settings\n")
+
+	// Initialize beads at rig level
+	fmt.Printf("  Initializing beads database...\n")
+	if err := m.initBeads(rigPath, opts.BeadsPrefix); err != nil {
+		return nil, fmt.Errorf("initializing beads: %w", err)
+	}
+	fmt.Printf("   ✓ Initialized beads (prefix: %s)\n", opts.BeadsPrefix)
+
 	// Create rig-level agent beads (witness, refinery) in rig beads.
 	// Town-level agents (mayor, deacon) are created by gt install in town beads.
 	if err := m.initAgentBeads(rigPath, opts.Name, opts.BeadsPrefix); err != nil {