I have described the differences between the world the character lives
in and the world the character is reading about, but it seems really
rushed, like he'd only been reading for a few minutes.
This sounds like possibly a case for Show; Don't tell.
Try not connecting the dots for the reader. Instead present the info from the story-within-the-story without drawing any comparison (from narrator or MC) –– it's just escapist entertainment (or school studies).
Later some of the MC's scenes or dialog could mirror the fiction, and then potentially the MC remembers the story and makes the direct comparison. MC can also hang a lampshade on the differences: "It's just like in the book, only I can't use a magic wand to fix the problem."
The inverse could be that we see the MC's life scenes first, and the fiction begins to mirror the real situations to the MC –– in other words, the fictional story is initially simplistic but begins to resemble familiar scenarios, and that's helped along by the MC's imagination. The MC might be biased against certain fictional characters, transferring feelings about the real person which they can't yet verbalize.
I could write "He read for a few hours before..." but it also seems kind of hurried....
Again, I suggest Show; Don't tell. If this realization is meant to have impact on the reader, it needs to engage the reader's interest and focus. Allow readers to draw their own comparisons more in pace with the MC, and give the MC some breathing room as they come to these conclusions too.