refactor: integrate chat persistence into Room

Move SaveMessage/LoadMessages logic into Room as private methods.
NewPersistentRoom auto-loads history and auto-saves on Send, removing
the need for handlers to coordinate persistence separately.

features/snakegame/handlers.go

@@ -126,7 +126,7 @@ func HandleSnakeEvents(snakeStore *snake.SnakeStore, nc *nats.Conn, sm *scs.Sess
 		var room *chat.Room
 
 		if sg.Mode == snake.ModeMultiplayer {
-			room = chat.NewRoom(nc, "snake.chat."+gameID, nil)
+			room = chat.NewRoom(nc, "snake.chat."+gameID)
 			chatCh, chatSub, err = room.Subscribe()
 			if err != nil {
 				return
@@ -247,7 +247,7 @@ func HandleSendChat(snakeStore *snake.SnakeStore, nc *nats.Conn, sm *scs.Session
 			Message:  signals.ChatMsg,
 		}
 
-		room := chat.NewRoom(nc, "snake.chat."+gameID, nil)
+		room := chat.NewRoom(nc, "snake.chat."+gameID)
 		room.Send(msg)
 
 		sse := datastar.NewSSE(w, r)