fix(billing): recognize cached tokens in OpenAI Responses API usage

The Responses API reports usage in its own dialect:
  input_tokens: 9434                       (inclusive grand total)
  input_tokens_details.cached_tokens: 8704 (cached subset)

normalize_usage only knew prompt_tokens_details (chat completions),
Anthropic top-level fields, and DeepSeek hit/miss. For /v1/responses
payloads it found no cache fields and, seeing no prompt_tokens key,
fell into the Anthropic-native branch that treats input_tokens as
excluding cache — so cached tokens were billed at the full input rate
and cache_read_input_tokens was recorded as 0.

Two changes:

* _extract_cache_tokens also reads input_tokens_details.cached_tokens
  and input_tokens_details.cache_write_tokens.
* normalize_usage treats input_tokens as an inclusive grand total when
  input_tokens_details is present (Anthropic native never sends that
  object, so it safely disambiguates the field-name collision).

Fixes both streaming and non-streaming /v1/responses billing, which
share calculate_cost -> normalize_usage.

routstr/payment/usage.py

@@ -15,6 +15,9 @@ names and in whether cached tokens are included in the input count:
   top-level, additive to (not included in) ``input_tokens``.
 * DeepSeek: ``prompt_cache_hit_tokens`` / ``prompt_cache_miss_tokens``, with
   ``prompt_tokens = hit + miss``.
+* OpenAI Responses API: ``input_tokens_details.cached_tokens`` (and
+  ``cache_write_tokens``), included in ``input_tokens`` — same inclusive
+  semantics as ``prompt_tokens``, but under the Responses API field names.
 
 What decides whether cached tokens must be subtracted out of the input count is
 **which prompt field the vendor uses**, not which cache field appears:
@@ -22,6 +25,10 @@ What decides whether cached tokens must be subtracted out of the input count is
 * ``prompt_tokens`` present -> cached + cache-write tokens are *included* in it
   (OpenAI family, DeepSeek, OpenRouter, litellm); subtract both so
   ``input_tokens`` holds only the regular-rate portion.
+* ``input_tokens_details`` present -> OpenAI Responses API; ``input_tokens``
+  *includes* cached + cache-write tokens, so subtract both. This disambiguates
+  the field-name collision with Anthropic native, which never sends
+  ``input_tokens_details``.
 * only ``input_tokens`` (Anthropic native) -> cached tokens are *additive*;
   leave ``input_tokens`` untouched.
 
@@ -78,6 +85,8 @@ def _extract_cache_tokens(usage_data: dict) -> tuple[int, int]:
     * Nested ``prompt_tokens_details``: ``cached_tokens`` for reads;
       ``cache_creation_tokens`` (litellm) or ``cache_write_tokens``
       (OpenRouter) for writes.
+    * Nested ``input_tokens_details`` (OpenAI Responses API): ``cached_tokens``
+      for reads, ``cache_write_tokens`` for writes.
     * DeepSeek: ``prompt_cache_hit_tokens`` for reads (no write concept).
     """
     cache_read = parse_token_count(usage_data.get("cache_read_input_tokens", 0))
@@ -92,6 +101,13 @@ def _extract_cache_tokens(usage_data: dict) -> tuple[int, int]:
                 prompt_details, "cache_creation_tokens", "cache_write_tokens"
             )
 
+    input_details = usage_data.get("input_tokens_details")
+    if isinstance(input_details, dict):
+        if not cache_read:
+            cache_read = parse_token_count(input_details.get("cached_tokens", 0))
+        if not cache_write:
+            cache_write = parse_token_count(input_details.get("cache_write_tokens", 0))
+
     if not cache_read:
         # DeepSeek: prompt_tokens = prompt_cache_hit_tokens + prompt_cache_miss_tokens
         cache_read = parse_token_count(usage_data.get("prompt_cache_hit_tokens", 0))
@@ -103,16 +119,16 @@ def normalize_usage(usage_data: object) -> NormalizedUsage | None:
     """Map a vendor usage dict onto the canonical shape, or None if absent.
 
     Cached reads and writes are subtracted from the input count exactly once,
-    only for dialects that report a ``prompt_tokens`` grand total that already
+    only for dialects whose input grand total already includes them: the
-    includes them (OpenAI family, DeepSeek, OpenRouter, litellm). Anthropic
+    ``prompt_tokens`` family (OpenAI chat completions, DeepSeek, OpenRouter,
-    native reports them additively under ``input_tokens`` and is left untouched.
+    litellm) and the OpenAI Responses API (``input_tokens`` inclusive,
+    identified by the presence of ``input_tokens_details``). Anthropic native
+    reports them additively under ``input_tokens`` and is left untouched.
     """
     if not isinstance(usage_data, dict):
         return None
 
-    output_tokens = _first_token_count(
+    output_tokens = _first_token_count(usage_data, "completion_tokens", "output_tokens")
-        usage_data, "completion_tokens", "output_tokens"
-    )
     cache_read, cache_write = _extract_cache_tokens(usage_data)
 
     # ``prompt_tokens`` is the inclusive grand total; ``input_tokens`` (Anthropic
@@ -120,6 +136,12 @@ def normalize_usage(usage_data: object) -> NormalizedUsage | None:
     if "prompt_tokens" in usage_data:
         input_tokens = parse_token_count(usage_data.get("prompt_tokens", 0))
         input_tokens = max(0, input_tokens - cache_read - cache_write)
+    elif isinstance(usage_data.get("input_tokens_details"), dict):
+        # OpenAI Responses API: ``input_tokens`` is also an inclusive grand
+        # total (cached tokens are a subset of it), signalled by the nested
+        # ``input_tokens_details`` object Anthropic native never sends.
+        input_tokens = parse_token_count(usage_data.get("input_tokens", 0))
+        input_tokens = max(0, input_tokens - cache_read - cache_write)
     else:
         input_tokens = parse_token_count(usage_data.get("input_tokens", 0))
 

tests/unit/test_usage_normalization.py

@@ -92,6 +92,58 @@ from routstr.payment.usage import NormalizedUsage, normalize_usage
                 cache_write_tokens=2000,
             ),
         ),
+        # OpenAI Responses API: cached tokens nested under input_tokens_details
+        # and INCLUDED in input_tokens (same semantics as prompt_tokens) →
+        # subtracted. Real payload shape from /v1/responses response.completed.
+        (
+            {
+                "input_tokens": 9434,
+                "input_tokens_details": {
+                    "cached_tokens": 8704,
+                    "cache_write_tokens": 0,
+                },
+                "output_tokens": 9,
+                "output_tokens_details": {"reasoning_tokens": 0},
+                "total_tokens": 9443,
+            },
+            NormalizedUsage(
+                input_tokens=730,
+                output_tokens=9,
+                cache_read_tokens=8704,
+                cache_write_tokens=0,
+            ),
+        ),
+        # OpenAI Responses API without a cache hit: input_tokens untouched.
+        (
+            {
+                "input_tokens": 9412,
+                "input_tokens_details": {
+                    "cached_tokens": 0,
+                    "cache_write_tokens": 0,
+                },
+                "output_tokens": 11,
+                "total_tokens": 9423,
+            },
+            NormalizedUsage(input_tokens=9412, output_tokens=11),
+        ),
+        # OpenAI Responses API with cache writes: both reads and writes are
+        # included in input_tokens → both subtracted.
+        (
+            {
+                "input_tokens": 1000,
+                "input_tokens_details": {
+                    "cached_tokens": 400,
+                    "cache_write_tokens": 200,
+                },
+                "output_tokens": 50,
+            },
+            NormalizedUsage(
+                input_tokens=400,
+                output_tokens=50,
+                cache_read_tokens=400,
+                cache_write_tokens=200,
+            ),
+        ),
         # litellm-normalized Anthropic: prompt_tokens is the grand total and the
         # write field is named cache_creation_tokens; top-level fields mirror it.
         # prompt_tokens present → both subtracted (NOT additive like native).