I imagine that in this case, she pulled a piece of tech out of her head. Much like Pearl did with the mirror in season one.

However, I have my own theory about gems and weapons. Weapons only appear after years of training.

For example ruby and sapphire don't have weapons as far as we have seen, but Garnet does. Even when Ruby fused with two other ones to make a big ruby, they didn't use a weapon. But they also remained fused for god knows how long. Chances are they learned how to create a weapon during that time.

Pearl could have learned from Rose before the rebellion began. Amethyst would have learned after she emerged from kindergarten.

Jasper was aware of Rose's existence, therefore she is probably as old as Pearl, give or take. She would have plenty of time to learn to summon one on her own.

The odd gem out in this scenario would be Lapis, who uses water instead of an actual weapon. But Lapis obviously isn't a normal gem.

Although I have another theory to explain why she isn't normal. It seems that important and powerful gems have two names instead of just one. Garnet, Pearl, Amethyst, etc. all have only one name. Hell, even Alexandrite, a four gem fusion, only has one name.

But then we get Yellow/Blue Diamond, Rose Quartz, and Lapis Lazuli, all of which are given two names. The first three are leaders and are also probably very powerful.

But Lapis has not been shown to be a leader. Yet, she was imprisoned for god knows how long for whatever reason. Even with a broken gem, she had the power to create an entire pillar of water out of the whole damn ocean.

But these are only theories and I have been wrong before.