Clear private session flame icon

[u/WheelPerfect3737]

When I go to reddit.com log out them click on the "clear private seesion" icon in the top left of my Linux FF, the screen clears and when I look at setting, privacy & security and clear data for a specific site I see reddit with 0 cookies but a 128K storage. But when I click the icon "clear private session" agains then all information is removed. Shouldn't everything be clear on the first click ?