I have the following snippet that (I think) defines a method addNumber1(x:T):T on a generic type T which is a subtype of AnyVal and h
I think the problem has nothing to do with AnyVal, AnyRef Or Any.
addNumber1(new Foo("1"))
This works because you indeed defined a Foo class that provides an implementation of def +(s:Int):T.
addNumber1(1)
This doesn't work because Integer class doesn't provide it, as is mentioned in the exception:
java.lang.NoSuchMethodException: java.lang.Integer.$plus(int)