Log every model call's time and tokens

Each call through BudgetedClient emits llm.call: seconds, input,
output and cached tokens, and the answering model when a fallback
answered; a failed call logs how long it ran before it failed.
Usage now carries the server's cached-prompt count on both routes.

Co-Authored-By: Claude Opus 5.5 (1M context) <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01J5Utyfzw7gF7UhjRDEtjTk

nisse-core/tests/test_llm.py

@@ -484,6 +484,48 @@ def test_the_answering_model_is_recorded() -> None:
     assert client.last_model == "gpt-test-1"
 
 
+def test_usage_includes_what_the_server_reused_from_its_cache() -> None:
+    client = make_client(
+        lambda request: httpx.Response(
+            200,
+            json={
+                "model": "qwen",
+                "choices": [{"message": {"role": "assistant", "content": "hi"}}],
+                "usage": {
+                    "prompt_tokens": 900,
+                    "completion_tokens": 40,
+                    "prompt_tokens_details": {"cached_tokens": 800},
+                },
+            },
+        )
+    )
+    client.complete(EVENTS, tools=None, model="qwen")
+    assert client.last_usage == {"input": 900, "output": 40, "cached": 800}
+
+    passthrough = AnthropicPassthroughClient(
+        "https://litellm.test",
+        "tok",
+        transport=httpx.MockTransport(
+            lambda request: httpx.Response(
+                200,
+                json={
+                    "model": "claude-opus-5-5",
+                    "stop_reason": "end_turn",
+                    "content": [{"type": "text", "text": "hi"}],
+                    "usage": {
+                        "input_tokens": 50,
+                        "output_tokens": 7,
+                        "cache_read_input_tokens": 30,
+                    },
+                },
+            )
+        ),
+        sleep=lambda _s: None,
+    )
+    passthrough.complete(EVENTS, tools=None, model="claude-opus-5-5")
+    assert passthrough.last_usage == {"input": 50, "output": 7, "cached": 30}
+
+
 # --- outages delay, never fail (L5) --------------------------------------------