Thanks Hans for that hint and the link to StackExchange. This looks pretty strange, but it works and I can understand why. Nevertheless I don't understand why standard AbsoluteOptions do not work.

This works for me:

g = Graphics3D[{Cube[]}, ImageSize -> Small]
Dynamic[AbsoluteOptions[g]]

I might be misunderstanding what you are wanting to do.

One interpretation of what information you are trying to get (from my own personal experience of messing with the 3D plots) is that you want the ViewVector property to update in real time when you are interacting with the plot. I've tried similar solutions to the one from Hans Milton below in the past without success (at least in the cloud notebooks - may it works on the local wolfram app? - I haven't tried b/c I just wanted to stick with the cloud version)

Part of the issue is that when you are manipulating the plot in the output viewer - I believe this ViewPoint is related to some property on the FrontEnd and is not actually changing the ViewVector property of the underlying graphics3D object.

This is a solution that I came up with recently that mostly worked for me. It's not perfect but it at least lets you rotate the 3D plot. Just replace g1 with whatever you are trying to plot. The cool thing about this is that you don't have to replot g1 with the new ViewPoint property. You can just use the new Graphics object g2.

g1 = Graphics3D[{Sphere[],Cuboid[]}];
    Manipulate[With[{v = RotationTransform[\[Theta]z[[1]]*-2Pi+Pi, {0, 0, 1}][{Pi, 0,Pi}]}, 
            g2= Show[g1, ViewPoint -> {v[[1]],v[[2]],\[Theta]z[[2]]*-40+20}, 
         SphericalRegion -> True]],{{\[Theta]z,{.5,.5}},Locator}]
Dynamic[Options[g2,ViewPoint]]
Dynamic[Show[g2]]