Jason, if this helps:
Zoom's automated AI "Live Transcription" only works in the main room;
If you also "assign a participant to type" BEFORE you open the breakout rooms, that individual can continue to type closed captions in whichever breakout rooms they join, even if they move to a different room. Zoom's live transcription will continue to work in the main room even after breakout rooms are open and the assigned participant is typing captions in their breakout room.
What I didn't check was which of these would be dominant in the main room when both live transcription is turned on and a captioner is assigned to type. Hopefully one of them will work!