fix(proxy): correct usage accounting on format-conversion paths

Audited all proxy format-conversion paths (Chat<->Message, Chat<->Response,
Gemini<->Message) for usage/cache metering. Five issues found and fixed.
The dedup mechanism (request_id PK, proxy/session source isolation) is
untouched, so no double-counting is introduced.

- A (Claude + openai_chat, streaming): inject stream_options.include_usage
  so OpenAI-compatible upstreams emit usage in the SSE tail. Without it the
  converted Anthropic message_delta was all-zero and the whole request's
  input/output/cache was dropped. Same root cause as the already-fixed
  Codex Chat path; the injection is extracted into a shared helper
  (transform::inject_openai_stream_include_usage) reused by both paths.

- C (Claude + gemini_native): subtract cachedContentTokenCount from
  input_tokens in build_anthropic_usage so input becomes fresh input
  (Anthropic semantics). Previously the cache-hit tokens were billed twice
  because this path meters as app_type="claude" (input_includes_cache_read
  = false) while Gemini's promptTokenCount includes the cache.

- D (Codex + openai_chat, streaming): gate log_usage on
  has_billable_tokens() to skip the synthetic all-zero usage the converter
  emits when a non-compliant upstream omits usage, preventing empty-row
  request-count inflation.

- P2 (from_claude_stream_events): use has_billable_tokens() for the return
  gate instead of input>0||output>0, so a fully-cached streamed request
  (cache_read>0, input==output==0) is still recorded. Affects all
  Claude-streaming paths, not just Gemini.

- P3 (Codex Chat->Responses, non-streaming): apply the same
  has_billable_tokens() filter the streaming branch got, since the
  synthesized all-zero usage makes from_codex_response return Some and
  bypass the `if let Some` guard.

Add TokenUsage::has_billable_tokens() as the unified predicate. New tests
cover include_usage injection, gemini input subtraction, the gate itself,
cache-only stream recording, and synthetic all-zero codex usage.
Full lib suite: 1569 passed.

src-tauri/src/proxy/providers/claude.rs

@@ -409,6 +409,10 @@ pub fn transform_claude_request_for_api_format(
             {
                 result["prompt_cache_key"] = serde_json::json!(key);
             }
+            // 流式请求必须注入 stream_options.include_usage，否则 OpenAI 兼容上游
+            // 不在 SSE 末尾吐 usage → 转换出的 Anthropic message_delta 全 0 →
+            // 整笔 input/output/cache 漏记（与 Codex Responses→Chat 路径同源）。
+            super::transform::inject_openai_stream_include_usage(&mut result);
             Ok(result)
         }
         "gemini_native" => super::transform_gemini::anthropic_to_gemini_with_shadow(
@@ -1617,6 +1621,43 @@ mod tests {
         assert!(transformed.get("max_output_tokens").is_some());
     }
 
+    #[test]
+    fn test_transform_claude_request_openai_chat_streaming_injects_include_usage() {
+        let provider = create_provider(json!({
+            "env": { "ANTHROPIC_BASE_URL": "https://openrouter.ai/api/v1" }
+        }));
+        // 流式请求必须注入 stream_options.include_usage，否则 OpenAI 兼容上游不在
+        // SSE 末尾吐 usage → 转换出的 Anthropic message_delta 全 0 → 整笔 usage 漏记。
+        let body = json!({
+            "model": "moonshotai/kimi-k2",
+            "messages": [{ "role": "user", "content": "hello" }],
+            "max_tokens": 128,
+            "stream": true
+        });
+        let transformed =
+            transform_claude_request_for_api_format(body, &provider, "openai_chat", None, None)
+                .unwrap();
+        assert_eq!(transformed["stream"], true);
+        assert_eq!(transformed["stream_options"]["include_usage"], true);
+    }
+
+    #[test]
+    fn test_transform_claude_request_openai_chat_non_streaming_omits_stream_options() {
+        let provider = create_provider(json!({
+            "env": { "ANTHROPIC_BASE_URL": "https://openrouter.ai/api/v1" }
+        }));
+        // 非流式请求不应注入 stream_options（usage 在非流式响应体里恒有）。
+        let body = json!({
+            "model": "moonshotai/kimi-k2",
+            "messages": [{ "role": "user", "content": "hello" }],
+            "max_tokens": 128
+        });
+        let transformed =
+            transform_claude_request_for_api_format(body, &provider, "openai_chat", None, None)
+                .unwrap();
+        assert!(transformed.get("stream_options").is_none());
+    }
+
     #[test]
     fn test_transform_claude_request_for_codex_oauth_uses_session_cache_key() {
         let provider = create_provider_with_meta(