I reckon most artistic depictions of Ancient Greeks comes from Medieval and later paintings. For instance https://www.history.com/.amp/topics/ancient-history/plato the image shows Plato writing something onto a page in a book. But did they actually have books like with spine and bound pages? I always imagine scrolls or leaves (loose paper not tree leaves).
In short, no. Scrolls were the norm for written material in Plato’s day.
The codex (book) came about in the Roman world, Silver Age. The general consensus is that the codex (initially, a labor- and cost-intensive alternative to the scroll, but easier to use) rose in popularity with early Christians, as they were better suited for travel. The codex eventually displaced the scroll for other civil purposes presumably for its utility. By Late Antiquity, scrolls were rarely used.
Raphael, in the painting shown at the link you share, was using items familiar to his contemporaries to illustrate the “School of Athens.”