This looks good so far. I can’t tell from the clip that you are gripping the pick tightly. Why are you doing that, as a way to “stop the thumb”? I don’t think that’s going to do it. What you really want to do is simply not give the thumb any reason to do anything. So it’s less of a focus on “stopping the thumb” and more of a focus on “doing a wrist movement”, if that makes any sense.
One thing you can try is using a grip more similar to what I’m using in the tutorial:
This will put the thumb flat up against the side of the index, and close up that gap. The point of this is twofold. One, in that position there’s less the thumb and index can do, so you may feel less need for them to “want” to move. And two, it’s different than what you’re currently doing, so it may have less interference or baggage. You don’t have to want to play this way, but you can use it as a way of getting the feeling of wrist-only in your mind.
This raises the question of why we would ever ask a person to play a specific way, instead of the way they already play which is habituated for them. In the past it was always “do what works for you”, where the way you already play becomes this sacrosanct thing that can’t be touched, because it is somehow specific to your body and “natural” for you. And I think that sentiment has generally been overblown.
At least one good argument for doing something a specific way is because it can make it possible for you to learn something you want to learn, when interference from your other ways of doing things have become a mental block. If you cannot get the feel of “all wrist, relaxed fingers” the way you are currently playing, then perhaps switching up the grip can help you zero in on what that feels like. Once that’s in your mind, you may be able to go back to the other grip while keep that mental image of “wrist movement”.