feat: implement Agent Chat Widget for entity pages

TASK_PHASE_AGENT_CHAT_WIDGET_MVP.md completed:

Backend:
- Add /api/v1/agents/{agent_id}/chat-room endpoint
- Add /api/v1/nodes/{node_id}/chat-room endpoint
- Add /api/v1/microdaos/{slug}/chat-room endpoint

Frontend:
- Create AgentChatWidget.tsx floating chat component
- Integrate into /agents/:agentId page
- Integrate into /nodes/:nodeId page
- Integrate into /microdao/:slug page

Ontology rule implemented:
'No page without agents' = ability to directly talk to agents on that page

services/city-service/routes_city.py

@@ -1255,6 +1255,158 @@ async def chat_bootstrap(
     }
 
 
+# =============================================================================
+# Chat Room API (TASK_PHASE_AGENT_CHAT_WIDGET_MVP)
+# =============================================================================
+
+@api_router.get("/agents/{agent_id}/chat-room")
+async def get_agent_chat_room(agent_id: str):
+    """
+    Отримати інформацію про кімнату чату для агента.
+    Повертає room_id, agent info для ініціалізації чату.
+    """
+    try:
+        agent = await repo_city.get_agent_by_id(agent_id)
+        if not agent:
+            raise HTTPException(status_code=404, detail=f"Agent not found: {agent_id}")
+        
+        # Get agent's primary room or create room slug
+        room_slug = f"agent-console-{agent.get('public_slug') or agent_id}"
+        room = await repo_city.get_room_by_slug(room_slug)
+        
+        # If room doesn't exist, try to get agent's primary room from dashboard
+        if not room:
+            rooms = await repo_city.get_agent_rooms(agent_id)
+            if rooms and len(rooms) > 0:
+                room = rooms[0]
+                room_slug = room.get("slug", room_slug)
+        
+        return {
+            "agent_id": agent_id,
+            "agent_display_name": agent.get("display_name"),
+            "agent_avatar_url": agent.get("avatar_url"),
+            "agent_status": agent.get("status", "offline"),
+            "agent_kind": agent.get("kind"),
+            "room_slug": room_slug,
+            "room_id": room.get("id") if room else None,
+            "matrix_room_id": room.get("matrix_room_id") if room else None,
+            "chat_available": room is not None and room.get("matrix_room_id") is not None
+        }
+    except HTTPException:
+        raise
+    except Exception as e:
+        logger.error(f"Failed to get agent chat room for {agent_id}: {e}")
+        raise HTTPException(status_code=500, detail="Failed to get agent chat room")
+
+
+@api_router.get("/nodes/{node_id}/chat-room")
+async def get_node_chat_room(node_id: str):
+    """
+    Отримати інформацію про кімнату чату для ноди.
+    Повертає room_id, guardian/steward agents info.
+    """
+    try:
+        node = await repo_city.get_node_by_id(node_id)
+        if not node:
+            raise HTTPException(status_code=404, detail=f"Node not found: {node_id}")
+        
+        # Get node support room
+        node_slug = node_id.replace("node-", "").replace("-", "_")
+        room_slug = f"node-support-{node_slug}"
+        room = await repo_city.get_room_by_slug(room_slug)
+        
+        # Get guardian and steward agents
+        guardian_agent = None
+        steward_agent = None
+        
+        if node.get("guardian_agent"):
+            guardian_agent = {
+                "id": node["guardian_agent"].get("id"),
+                "display_name": node["guardian_agent"].get("name"),
+                "kind": node["guardian_agent"].get("kind"),
+                "role": "guardian"
+            }
+        
+        if node.get("steward_agent"):
+            steward_agent = {
+                "id": node["steward_agent"].get("id"),
+                "display_name": node["steward_agent"].get("name"),
+                "kind": node["steward_agent"].get("kind"),
+                "role": "steward"
+            }
+        
+        return {
+            "node_id": node_id,
+            "node_name": node.get("name"),
+            "node_status": node.get("status", "offline"),
+            "room_slug": room_slug,
+            "room_id": room.get("id") if room else None,
+            "matrix_room_id": room.get("matrix_room_id") if room else None,
+            "chat_available": room is not None and room.get("matrix_room_id") is not None,
+            "agents": [a for a in [guardian_agent, steward_agent] if a is not None]
+        }
+    except HTTPException:
+        raise
+    except Exception as e:
+        logger.error(f"Failed to get node chat room for {node_id}: {e}")
+        raise HTTPException(status_code=500, detail="Failed to get node chat room")
+
+
+@api_router.get("/microdaos/{slug}/chat-room")
+async def get_microdao_chat_room(slug: str):
+    """
+    Отримати інформацію про кімнату чату для MicroDAO.
+    Повертає room_id, orchestrator agent info.
+    """
+    try:
+        dao = await repo_city.get_microdao_by_slug(slug)
+        if not dao:
+            raise HTTPException(status_code=404, detail=f"MicroDAO not found: {slug}")
+        
+        # Get MicroDAO lobby room
+        room_slug = f"microdao-lobby-{slug}"
+        room = await repo_city.get_room_by_slug(room_slug)
+        
+        # If no lobby room, try to get primary room
+        if not room:
+            rooms = await repo_city.get_microdao_rooms(dao["id"])
+            if rooms and len(rooms) > 0:
+                # Find primary room or first room
+                primary = next((r for r in rooms if r.get("room_role") == "primary"), rooms[0])
+                room = primary
+                room_slug = room.get("slug", room_slug)
+        
+        # Get orchestrator agent
+        orchestrator = None
+        orchestrator_id = dao.get("orchestrator_agent_id")
+        if orchestrator_id:
+            orch_agent = await repo_city.get_agent_by_id(orchestrator_id)
+            if orch_agent:
+                orchestrator = {
+                    "id": orchestrator_id,
+                    "display_name": orch_agent.get("display_name"),
+                    "avatar_url": orch_agent.get("avatar_url"),
+                    "kind": orch_agent.get("kind"),
+                    "role": "orchestrator"
+                }
+        
+        return {
+            "microdao_id": dao["id"],
+            "microdao_slug": slug,
+            "microdao_name": dao.get("name"),
+            "room_slug": room_slug,
+            "room_id": room.get("id") if room else None,
+            "matrix_room_id": room.get("matrix_room_id") if room else None,
+            "chat_available": room is not None and room.get("matrix_room_id") is not None,
+            "orchestrator": orchestrator
+        }
+    except HTTPException:
+        raise
+    except Exception as e:
+        logger.error(f"Failed to get microdao chat room for {slug}: {e}")
+        raise HTTPException(status_code=500, detail="Failed to get microdao chat room")
+
+
 # =============================================================================
 # City Feed API
 # =============================================================================