Empty model could reach the API on a recovery turn after stream_interrupt_abort,
failing HTTP 400 "No models provided" with no recovery — the session went
silent until the user manually re-sent (#35314).
- gateway/run.py: cache last-successfully-resolved model per session (+ a
process-wide slot); when a fresh config read returns an empty model on a
recovery turn, reuse the last-known-good instead of building model="".
- run_agent.py + agent/conversation_loop.py: only emit "trying fallback..."
status when a fallback chain actually exists, so the UI stops announcing a
fallback that will never run (also #17446).
- tests: empty-model recovery + _has_pending_fallback gate.