Along with the new homepage design being released today, just like I suspected you can now play the PSA Missions on Club Penguin’s website. Unlike before when they were in the Club Penguin game, you do not need to beat the previous mission in order to play the next one. on the bottom right of Club Penguin’s Fun Stuff section there is an image you need to click called ‘Play PSA Missions’.
From there you can select which one:
Each mission page has the mission at the top of the page, then below it is a quick outline of the mission.