How would you create a sticky drawer/bottom drawer/slide-out component with MUI?

I'm using MUI v5, and I'm not entirely sure what this type of UI is called (where there's a drawer-like/slide-out component in the bottom right hand of your screen):

Name of component aside, how would I build this with MUI? Would it be best to use the <Drawer /> component, or some other UI element for it?