This description in the rules leaves me confused. Are segmented runs allowed, or do we just record our break.

segmented subchapters and full segmented runs both have a category of their own

"breaks can be taken between (,,,)" is to allow runners to pause between chapters since in New Game+ categories the time is counted by IGT you are allowed to stop playing between chapters, though the recording, as stated, cannot have any section of it removed (or in other words, edited) if it is being submitted to the Singe Segment (or SS) category

tl;dr answer: you can take a break, just record it if it's Single Segment