feat(rooms): FFA AFK heartbeat — synthetic [no message] to let rooms run unattended

[Flare576]

Summary

In FFA rooms, allow a room to keep running without the human actively responding by injecting a synthetic [no message] human turn — so personas can just... talk to each other.

Design Notes

• Room-level setting to enable AFK mode
• When human hasn't responded within a configurable idle window, inject a silent human message (e.g. silence_reason: '[no message]') to unblock the next round of persona responses
• No LLM call needed for the human turn — purely synthetic
• Personas respond naturally to each other; human can re-engage at any time
• Simplest implementation: a threshold + the existing silence injection path

Open Questions

• Should there be a max-rounds guard to prevent infinite loops?
• UI to indicate the room is in AFK mode vs. waiting for human?