So, back in like the very first episode “Gem Glow”, we learn that Pearl summons her weapon through hard work and dedication and Amethyst summons hers whenever she wants to.
“Sworn to the Sword” implies that Pearl’s role in gem society was never to be combat oriented. Which means its entirely possible she was never meant to summon a weapon at all. That would mean she does it so easily now is entirely because of how hard she trained to do so, so she could fight alongside and protect Rose. In that same vein, it might explain why Peridot is never seen summoning her own weapon, since she seems to have a similar role. “Hard work and dedication””
Unlike Pearl, Amethyst is implied to have been created mainly for the purpose of fighting. That would explain why she can summon her weapon so easily compared to Pearl, it’s entirely what she was created for. “Whenever [she] needs to summon her weapon, it just happens”