If you took the LCD screen from a tablet. Segmented it into equally sized rectangles, and then added connection ports on the sides of each rectangle. Could you then separate and stack the rectangles on top of eachother to save space? And then fold it back out to create a tablet-sized screen again.
There is a foldable LED screen at CES this year that works similar to how you describe but 4 panels horizontally. The four panels fit so well that no join is visible.
It is called microLED, it's how mega gigantic and movable screens for events are made. It's completely modular and you can infinitely connect them to one another to make it essentially any size you want.
I saw "telescopic LCD" and thought of using those screens for telescopes. Am disappoint it's just folding LCD. I don't think it's feasible with those, specifically, due to their construction of film layer + liquid crystal + other film layer + backlight. Unless you're ok with essentially 4 separate smaller screens
I think your limiting factor would be bezels, so there would be a small gap between the screens. Plus this would be a mechanical nightmare to make cheap and durable