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/transform_gemini.rs

@@ -1101,7 +1101,7 @@ pub(crate) fn build_anthropic_usage(usage: Option<&Value>) -> Value {
         });
     };
 
-    let input_tokens = usage
+    let prompt_tokens = usage
         .get("promptTokenCount")
         .and_then(|value| value.as_u64())
         .unwrap_or(0);
@@ -1109,18 +1109,26 @@ pub(crate) fn build_anthropic_usage(usage: Option<&Value>) -> Value {
         .get("totalTokenCount")
         .and_then(|value| value.as_u64())
         .unwrap_or(0);
-    let output_tokens = total_tokens.saturating_sub(input_tokens);
+    let cached_tokens = usage
+        .get("cachedContentTokenCount")
+        .and_then(|value| value.as_u64())
+        .unwrap_or(0);
+    // Gemini 的 promptTokenCount 含缓存命中（cachedContentTokenCount）；而 Anthropic
+    // 语义下 input_tokens 必须是不含 cache 的 fresh input、cache_read 单列。本路径转成
+    // Anthropic 后以 app_type=claude 记账，calculator 对 claude 设 input_includes_cache_read
+    // =false 不再从 input 扣 cache，因此这里必须先扣减，否则缓存 token 会被双重计费
+    // （一次按完整 input 价、一次按 cache_read 价）。output 仍按 total-prompt 计算
+    // （prompt 是总输入，扣减只作用于 input/cache 的拆分，不影响 output）。
+    let input_tokens = prompt_tokens.saturating_sub(cached_tokens);
+    let output_tokens = total_tokens.saturating_sub(prompt_tokens);
 
     let mut result = json!({
         "input_tokens": input_tokens,
         "output_tokens": output_tokens
     });
 
-    if let Some(cached) = usage
-        .get("cachedContentTokenCount")
-        .and_then(|value| value.as_u64())
-    {
-        result["cache_read_input_tokens"] = json!(cached);
+    if cached_tokens > 0 {
+        result["cache_read_input_tokens"] = json!(cached_tokens);
     }
 
     result
@@ -1370,7 +1378,11 @@ mod tests {
         assert_eq!(result["content"][0]["type"], "text");
         assert_eq!(result["content"][0]["text"], "Hello from Gemini");
         assert_eq!(result["stop_reason"], "end_turn");
-        assert_eq!(result["usage"]["input_tokens"], 12);
+        // input_tokens = promptTokenCount(12) - cachedContentTokenCount(3) = 9（fresh input）。
+        // Gemini 的 promptTokenCount 含缓存命中，但 Anthropic 语义要求 input 不含 cache、
+        // cache_read 单列；二者相加(9+3)=总输入 12。扣减避免本路径以 app_type=claude
+        // 记账时把缓存 token 双重计费。
+        assert_eq!(result["usage"]["input_tokens"], 9);
         assert_eq!(result["usage"]["output_tokens"], 8);
         assert_eq!(result["usage"]["cache_read_input_tokens"], 3);
     }