Add a diarized meeting mode for continuous agent orchestration

It would be useful to have a meeting-oriented dictation mode that supports speaker diarization and continuously provides meeting context to an agent.

The mode could:

- Keep a raw, append-only transcript containing the speaker, timestamp, and text.
- Automatically send new transcript chunks to a dedicated agent session at regular intervals.
- Let the user provide a prompt describing what the agent should watch for or accomplish during the meeting.
- Have the dedicated session orchestrate work in other sessions instead of doing the work itself, so it remains responsive as new conversation arrives.
- Allow agents to act on discussed items while the meeting is still in progress.

This would be especially valuable for in-person office conversations and meetings, where an agent could continuously follow the discussion, capture action items, investigate questions, and start relevant work without requiring users to manually paste or submit each transcript segment.

Azure AI Speech already demonstrates speaker diarization in its speech-to-text playground, so this may be a useful foundation for the transcription side of the experience.