So I know this is an old post but I’ve just experienced something very similar to the original poster. Unfortunately for me I only bought the car second hand 7 months ago, but the sound in the video above sounds very similar. Car throws up error code P0335 and runs rough.
I wasn’t aware of the recall, but checking the Lexus recall checker shows this car does have an eligible recall. Will contact Lexus and see where that leads but if as above the quote is 2k just to diagnose then it may not be worth it.