Per-room AI provider/model selection

I want to set the AI provider and model per room. The global setting should only be the default for new rooms.

Right now the provider is a single global switch: a room can only use models from the currently active profile. So if I want my work rooms on a company gateway and my personal rooms on my Claude subscription, I have to flip the global profile every time I switch rooms. That makes a clean work/personal separation across rooms impractical.

Threads already store the provider and model they're locked to — what's missing is being able to choose them per room.

No files or tests are named. Trace the current global provider/model setting, the existing thread provider/model persistence, and the room settings entry points. Done means each room can retain its selected provider and model, while the global setting remains the default only for newly created rooms.

Written by the indexing model from the issue text.