What Is This Shrub?

Hello !
I think it could also be a Cotinus coggygria, possibly it is the royal purple type. There are different types of Cotinus coggygria, some are american native some are european and China native, but it's been many centuries since the european types also grow in America.

The difference with a lagerstroemia is that most Cotinus coggygria are shrubs with a rough bark when I do not think that you can make a lagerstroemia grow as a bush. It is a tree with an incredibly smooth bark. Your plant grows as a shrub, very divided right from its foot even if, as it seems on the picture, it had two branches cut right from the foot, it still keeps growing with the shape of a shrub not of a tree it has no main trunk. In any case lagerstroemia or cotinus coggygria they are both beautiful. Cotinus coggygria is cold and heat resistant, grow fast and accomodates to poor soil. I think you could cut one of the leaves of your plant and go to a plant nursery to compare it to lagerstroemia or cotinus sold there. Leaves veins and shape make the difference.