Official PS2 online servers were shut down in 2016. You cannot play The Sims Castaway Stories (or any PS2 game) online via the original network.
Play The Sims 4 (free on PC/console) or The Sims 3 with mods for open-world storytelling. They offer deeper gameplay and modern multiplayer mods (e.g., The Sims 4 Multiplayer Mod by pancake).