The agent's own name (said to the caller, shown on the offer).
Who is on the other end of the room.
The user the call runs as (a taking-over agent runs as the same user).
Removes THIS agent from the room. The room, and the caller, stay.
Tells THIS agent's model something that happened out-of-band, so it can say it aloud.
The live room call one AI agent is part of, as the engine needs to act on it. The host builds one per agent session and hands it to RoomHandoffEngine.RequestHandoff.