“Old money” is more of a behavioral classification than a looks/aesthetic one… for example being flashy or bragging that you have money is considered very “new money” behavior, where as if you were raised in the generational wealth sphere, everyone has money so nobody really brags about it, it’s like bragging that you ate lunch today.

As to why influencers are labelling their look as ‘old money,’ it’s because it sells. It got you to click on the video. They found a niche of people who want to look rich and are providing instruction to do that on the very budget level you mention.