I need some help with notes and S Pen

I'm writing some math formulas and numbers on the notes screen that's created when I remove the S Pen.

I hold the home button to use Google AI to solve these math problems and display my results. It asks me to unlock the phone. After I do so, my notes disappear.

I can save the notes beforehand. If I pin them, I can't seem to find them again unless I lock the phone and try to pin a new note.

Is there any way to configure my locked and unlocked notes to cross over and allow me to do these things without having to save them?