So that class is extended by the Illuminate\Routing\Router class which then uses the Macroable trait in which the method mixin is defined. So again that's a method not a property.
And in the RouteRegistrar class you can see the __call method which acts whenever a method that does not exists on the parent class propagates the call to the child classes which in this case is as I said above the Router class that has the mixin method. I hope it is a bit more clear now.
I don't understand how the namespace is being set through the UrlGenerator and the controller actions are being formatted to incorporate the full namespace.
I believe the Builder pattern is used there, so you can take a look at that design pattern. Mainly you will need to check what the previous method returns, in your example above, you need to check what does Route::middleware('web') returns, that's where the namespace method exists so the call can be chained.