feat(doctor): add custom types check and centralize BeadsCustomTypes

- Add BeadsCustomTypes constant ("agent,role,rig,convoy,slot") to avoid
  hardcoded strings scattered across the codebase
- Add CustomTypesCheck to gt doctor that verifies Gas Town custom types
  are registered with beads, with --fix support
- Register custom types during gt init (best-effort, skips if no beads)
- Update install.go, rig_check.go, and rig/manager.go to use the constant

This ensures consistent type registration across all code paths and
catches misconfigured beads databases via gt doctor.

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

internal/constants/constants.go

@@ -73,6 +73,19 @@ const (
 	FileAccountsJSON = "accounts.json"
 )
 
+// Beads configuration constants.
+const (
+	// BeadsCustomTypes is the comma-separated list of custom issue types that
+	// Gas Town registers with beads. These types were extracted from beads core
+	// in v0.46.0 and now require explicit configuration.
+	BeadsCustomTypes = "agent,role,rig,convoy,slot"
+)
+
+// BeadsCustomTypesList returns the custom types as a slice.
+func BeadsCustomTypesList() []string {
+	return []string{"agent", "role", "rig", "convoy", "slot"}
+}
+
 // Git branch names.
 const (
 	// BranchMain is the default main branch name.