"Menu Storage" is a glitch that happens if you die during the stage clear animation. The retry menu will take priority over the Stage clear menu

Upon hitting retry, the stage complete menu will reappear. This is useful if you're going for RTA IL Records, (Not IGT) as you can warp out of the level immediately.

Additional side effect is that you can save whatever IGT you had when you hit the owl even though you died.

Current levels with Menu Storage ↑ 1-5 (Useful for IGT Aswell as RTA Timing)

↑ 2-4 (Haven't been able to get menu storage on film but i've gotten it before early in my playthrough.

Thank you for the documentation!

Updating this forum to include 4-s2, for sami as far as menu storage is concerned