The format for a formal proof is determined by the Nemeth Code. However, even within a statement/reason proof, only technical material belongs in "Nemeth bubbles."
See Lesson 12 of the Provisional Revised Nemeth Course Manual, posted by NFB for some examples. In particular, see pages 12–30 (for a sample transcription) and page 12–29 (for a sample transcriber's note).
Thank you for the question!
–Kyle