I’m thinking magic trick style. What if your laptop screen has real depth to it? And the objects inside are the real objects, and they just come out and it’ll look as if it was a screen because it is a screen of a laptop. It’ll depend on what’s on screen and the type of shots, but it feels like it could be doable this way. The laptop would have to be head on, if you look it from the side it’ll break the illusion.
Also if it’s a flat screen on the laptop, I would scale and squash the objects near to zero and just animate their visibility into view as they pop out of the screen and un-squash and stretch out of the screen.