This is a tough one!
Pages are hard because, while we know that they have lots of hidden potential, we’ve only seen pages that have so far failed at reaching theirs! At any rate, the best guess I’ve seen is that Pages are passive (+) Knights, who exploit/use/equip their aspect themselves. Pages, on the other hand, would start out weak, but gain strength through their training, inspiring others to equip the Page’s aspect themselves! We can see this through the prophecy Aranea told Jake - that he would one day (presumably after reaching his potential) defeat a version of Lord English (probably the possessed Jack), thereby giving others Hope! There’s also Peter Pan, who Tavros’ character arc and class was built on, who teaches young boys to detach themselves and fly away - giving them Breath! But that’s just theorizing on my part, so I’ll try to stick with what we know in this post; it will probably just come out infuriatingly vague, so I apologize in advance for that!
Space is the aspect of the literal backdrop of reality, but also of creation, creativity, reproduction, and metamorposis. A Page of Space, who has within them the potential of creation and physical reality would be unbelievably powerful, once their potential has been reached. He would probably start out somewhat unsure of his place in the world around him and what he can do/create, but a kernel of understanding would be there, which would grow as the session progressed, giving him more creativity and sureness in his place in the physical universe.
Space players so far have all seemed to become what they always wanted to be (metamorphosis), as happened with Jade becoming a furry and Kanaya and Porrim becoming Rainbow Drinkers, and Calliope likely becoming a troll if she ever ascends. A Page of Space’s metamorphosis upon reaching his potential would probably be drastic, the final realization of his creative potential, which might inspire his co-players to become what they’ve always wanted to be. A page of space might involve others in the frog breeding process, probably taking a very hands-off approach with that quest, inviting others to engage in the creation process.
That’s all I can think of for now! Sorry again if it’s vague and crap, it’s a very hard class to figure out.