Paper Mario's story progression is handled by a value that represents where you are in the story of the game. Certain events, such as picking up certain items, entering maps for the first time, etc, change this story value. This is the most relevant to Reverse All Cards, Glitchless, and No Major Sequence Breaks.

List of story triggers:

https://docs.google.com/document/d/1wrIhXo5cQjnUC_RcW8gETNvN2LJHpeuriV2NhhSUBwc/edit