when it says "Closing and opening the game mid-run is banned", does that mean closing the whole game (via switch home screen >> close software or pressing the exit button in windows) or does it ban going to the main menu and continuing the save file? or both?

I would think going to the main menu and continuing the same save would be fine, in the case of a soft lock or something like that, but it could be a huge time loss depending on where you are in the run.

But also I'm not a mod so I dunno for sure