fix(gateway): recover model on post-interrupt turn; gate fallback status (#35381)

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.

run_agent.py

@@ -3550,6 +3550,18 @@ class AIAgent:
         from agent.chat_completion_helpers import try_activate_fallback
         return try_activate_fallback(self, reason)
 
+    def _has_pending_fallback(self) -> bool:
+        """Whether a fallback provider is actually available to switch to.
+
+        Used to gate user-facing "trying fallback..." status so we don't
+        announce a fallback that will never be attempted (the user has no
+        fallback chain configured).  Mirrors the early-return guard in
+        ``try_activate_fallback`` (#35314, #17446).
+        """
+        chain = getattr(self, "_fallback_chain", None) or []
+        index = getattr(self, "_fallback_index", 0)
+        return index < len(chain)
+
     # ── Per-turn primary restoration ─────────────────────────────────────
 
     def _restore_primary_runtime(self) -> bool: