test(provider): pin api.anthropic.com host on fallback api_mode

Pins that a custom provider on the native api.anthropic.com host resolves to
anthropic_messages on the try_activate_fallback path. From #49247.

tests/run_agent/test_provider_fallback.py

@@ -182,6 +182,35 @@ class TestFallbackChainAdvancement:
             assert agent._try_activate_fallback() is True
             assert mock_rpc.call_args.kwargs["explicit_api_key"] == "env-secret"
 
+    def test_anthropic_host_custom_provider_uses_anthropic_messages(self):
+        """A custom provider on the native api.anthropic.com host (no
+        "/anthropic" path suffix, name != "anthropic") must resolve to the
+        anthropic_messages wire protocol — not default to chat_completions,
+        which POSTs /v1/chat/completions and 404s. Mirrors the primary-path
+        determine_api_mode() host check."""
+        fbs = [
+            {
+                "provider": "cron-anthropic",
+                "model": "claude-sonnet-4-6",
+                "base_url": "https://api.anthropic.com",
+                "key_env": "MY_FALLBACK_KEY",
+            }
+        ]
+        agent = _make_agent(fallback_model=fbs)
+        with (
+            patch.dict("os.environ", {"MY_FALLBACK_KEY": "env-secret"}, clear=False),
+            patch(
+                "agent.auxiliary_client.resolve_provider_client",
+                return_value=(
+                    _mock_client(base_url="https://api.anthropic.com"),
+                    "claude-sonnet-4-6",
+                ),
+            ),
+            patch("hermes_cli.model_normalize.normalize_model_for_provider", side_effect=lambda m, p: m),
+        ):
+            assert agent._try_activate_fallback() is True
+            assert agent.api_mode == "anthropic_messages"
+
 
 # ── Pool-rotation vs fallback gating (#11314) ────────────────────────────