Unless you have opted out of prompt history, you can retrieve your prompt activity whether you are logged in or not, by clicking "Prompt Activity" on the left-hand panel of Magisterium AI.
Note that logged out users are only able to view their prompt history if they do not clear or disable cookies in their browser. Prompt history for logged-out visitors is stored in a temporary cookie on your computer, and only lasts as long as the cookie does. Prompt history is stored indefinitely for logged in users. However, the prompt history can be entirely deleted.