if you have sapphire - then in the Distort effects is one called infinite zoom…that will give the zooming effect…but to get the screens showing the shot its not too difficult.
Feed the shot into an Action node, the duplicate the node for as many screens are needed - a quick bicubic for each image will let you put it into each screen. Then cut out the talent with a gmask and position that layer in front.
Next make a duplicate of the Action node and feed the same inputs with the output from Action 1. Essentially you are using Action 1 to create the camera, which is seeing the talent in all the screens, then Action two is applying the combined shot into every screen.
I only did the left side for speed and to try it out!
I’ve done this with UV’d geo for fun–I had a shot where we did an alembic track of a woman rolling out a piece of paper. We were going to change the paper’s graphic.
As a side project I kept applying the plate to the paper geo and rendering it over and over, making a recursive video of her rolling out the paper of her rolling out the paper. No one found it nearly as funny as I did, but ten years on I still think it was the greatest.
As others have said, you can do something similar with just cards. 3d track the shot and put cards where each TV is. Render that out, then copy the action and feed the result through, over and over. You won’t get any sort of analog weirdness which may be desirable, but you could put some filter on each layer to mimic generational loss.