Edit: Turns out it was not a bug, but rather me having the logic on all of my Visual Elements that caused the excessive events to be fired. When I constrain the debug to only one Visual Element everything works as expected.
Did some debugging and noticed that the runtime events were called too many times (and some at the wrong time). In my case, Mouse Over is called 4 times when I enter the element, Mouse Enter 3, and Mouse Out 1. When I click, Mouse Down is called 3 times, Mouse Over 3 times and Mouse Enter 3 times. When I exit the element, Mouse Over is called once, Mouse Enter is called once, Mouse Out is called 4 times and Mouse Leave is called 4 times. This is the relevant code:
VisualElement v = new VisualElement();
v.RegisterCallback<MouseOverEvent>(e => { Debug.Log("Mouse Over"); });
v.RegisterCallback<MouseEnterEvent>(e => { Debug.Log("Mouse Enter"); });
v.RegisterCallback<MouseLeaveEvent>(e => { Debug.Log("Mouse Leave"); });
v.RegisterCallback<MouseDownEvent>(e => { Debug.Log("Mouse Down"); });
v.RegisterCallback<MouseOutEvent>(e => { Debug.Log("Mouse Out"); });
Summary (In the order the events were called)
Enter:
Mouse Over = 4
Mouse Enter = 3
Mouse Out = 1
Click:
Mouse Down = 3
Mouse Over = 3
Mouse Enter = 3
Exit:
Mouse Over = 1
Mouse Enter = 1
Mouse Out = 4
Mouse Leave = 4