feat: Add presence heartbeat for Matrix online status

- matrix-gateway: POST /internal/matrix/presence/online endpoint
- usePresenceHeartbeat hook with activity tracking
- Auto away after 5 min inactivity
- Offline on page close/visibility change
- Integrated in MatrixChatRoom component

backend/domain/dao/dao.logic.ts

@@ -0,0 +1,30 @@
+/**
+ * Pure domain logic for DAO operations
+ * No I/O, no side effects
+ */
+
+import type { DaoRecord, DaoLevel, FederationMode } from './types';
+
+/**
+ * Check if DAO can become a SuperDAO
+ */
+export function canBecomeSuperDao(dao: DaoRecord, childCount: number): boolean {
+  return childCount >= 1 && dao.federationMode === 'none';
+}
+
+/**
+ * Check if DAO can join a federation
+ */
+export function canJoinFederation(dao: DaoRecord, targetLevel: DaoLevel): boolean {
+  // A3/A4 can join, exceptions for A2 handled by PDP
+  return (dao.level === 'A3' || dao.level === 'A4') && dao.federationMode === 'none';
+}
+
+/**
+ * Check if DAO can leave federation
+ */
+export function canLeaveFederation(dao: DaoRecord): boolean {
+  return dao.federationMode === 'member' && dao.parentDaoId !== null;
+}
+
+