feat: Add Chat API endpoints for Matrix integration

City Service:
- GET /api/v1/chat/rooms/{room_id}/messages - get message history
- POST /api/v1/chat/rooms/{room_id}/messages - send message
- Add get_room_by_id to repo_city

Synapse:
- Increase rate limits for room creation
- Add rc_joins, rc_invites configuration

All 27 rooms now have matrix_room_id

services/city-service/repo_city.py

@@ -142,6 +142,24 @@ async def get_room_by_slug(slug: str) -> Optional[dict]:
     return dict(row) if row else None
 
 
+async def get_room_by_id(room_id: str) -> Optional[dict]:
+    """Отримати кімнату по ID (UUID)"""
+    pool = await get_pool()
+    
+    query = """
+        SELECT 
+            cr.id, cr.slug, cr.name, cr.description, cr.is_default, cr.created_at, cr.created_by,
+            cr.matrix_room_id, cr.matrix_room_alias, cr.logo_url, cr.banner_url,
+            cr.microdao_id, m.name AS microdao_name, m.slug AS microdao_slug, m.logo_url AS microdao_logo_url
+        FROM city_rooms cr
+        LEFT JOIN microdaos m ON cr.microdao_id = m.id
+        WHERE cr.id = $1
+    """
+    
+    row = await pool.fetchrow(query, room_id)
+    return dict(row) if row else None
+
+
 async def create_room(
     slug: str, 
     name: str, 

services/city-service/routes_city.py

@@ -1589,6 +1589,102 @@ async def get_microdao_chat_room(slug: str):
         raise HTTPException(status_code=500, detail="Failed to get microdao chat room")
 
 
+# =============================================================================
+# Chat API (TASK_PHASE_MATRIX_FINALIZE_v2)
+# =============================================================================
+
+class SendMessageRequest(BaseModel):
+    body: str
+    sender: Optional[str] = None
+
+
+class ChatMessage(BaseModel):
+    event_id: str
+    sender: str
+    body: str
+    timestamp: int
+
+
+@api_router.get("/chat/rooms/{room_id}/messages")
+async def get_chat_messages(room_id: str, limit: int = 50):
+    """
+    Отримати історію повідомлень з Matrix кімнати.
+    room_id може бути slug або UUID кімнати.
+    """
+    try:
+        # Get room from DB
+        room = await repo_city.get_room_by_id(room_id)
+        if not room:
+            # Try by slug
+            room = await repo_city.get_room_by_slug(room_id)
+        
+        if not room:
+            raise HTTPException(status_code=404, detail=f"Room not found: {room_id}")
+        
+        matrix_room_id = room.get("matrix_room_id")
+        if not matrix_room_id:
+            raise HTTPException(status_code=400, detail="Room has no Matrix integration")
+        
+        # Get messages from Matrix via gateway
+        messages = await get_room_messages(matrix_room_id, limit=limit)
+        
+        return {
+            "room_id": room.get("id"),
+            "room_slug": room.get("slug"),
+            "matrix_room_id": matrix_room_id,
+            "messages": messages,
+            "count": len(messages)
+        }
+    except HTTPException:
+        raise
+    except Exception as e:
+        logger.error(f"Failed to get chat messages for {room_id}: {e}")
+        raise HTTPException(status_code=500, detail="Failed to get chat messages")
+
+
+@api_router.post("/chat/rooms/{room_id}/messages")
+async def send_chat_message(room_id: str, payload: SendMessageRequest):
+    """
+    Надіслати повідомлення в Matrix кімнату.
+    room_id може бути slug або UUID кімнати.
+    """
+    try:
+        # Get room from DB
+        room = await repo_city.get_room_by_id(room_id)
+        if not room:
+            # Try by slug
+            room = await repo_city.get_room_by_slug(room_id)
+        
+        if not room:
+            raise HTTPException(status_code=404, detail=f"Room not found: {room_id}")
+        
+        matrix_room_id = room.get("matrix_room_id")
+        if not matrix_room_id:
+            raise HTTPException(status_code=400, detail="Room has no Matrix integration")
+        
+        # Send message via gateway
+        event_id = await send_message_to_room(
+            room_id=matrix_room_id,
+            body=payload.body,
+            sender=payload.sender
+        )
+        
+        if not event_id:
+            raise HTTPException(status_code=500, detail="Failed to send message to Matrix")
+        
+        return {
+            "ok": True,
+            "event_id": event_id,
+            "room_id": room.get("id"),
+            "matrix_room_id": matrix_room_id
+        }
+    except HTTPException:
+        raise
+    except Exception as e:
+        logger.error(f"Failed to send chat message to {room_id}: {e}")
+        raise HTTPException(status_code=500, detail="Failed to send chat message")
+
+
 # =============================================================================
 # Presence API (TASK_PHASE_AGENT_PRESENCE_INDICATORS_MVP)
 # =============================================================================