After you load the game can you wait for a couple of minutes? Also for me on Sonoma, once the loaded game starts it is smooth, close to 60fps and no stuttering but as the GPU overheats the fans do NOT speed up and in around a minute or two it throttles and then it becomes very stuttery.
Let it run for some time after loading the save game and do not start a battle. That could be an interesting data point.
