feat: support cached input token billing

apps/api/internal/clients/helpers.go

@@ -185,11 +185,17 @@ func buildOpenAIStreamResult(last map[string]any, parts []string, reasoningParts
 		}},
 	}
 	if usage.TotalTokens > 0 {
-		out["usage"] = map[string]any{
+		usageMap := map[string]any{
 			"prompt_tokens":     usage.InputTokens,
 			"completion_tokens": usage.OutputTokens,
 			"total_tokens":      usage.TotalTokens,
 		}
+		if usage.CachedInputTokens > 0 {
+			usageMap["prompt_tokens_details"] = map[string]any{
+				"cached_tokens": usage.CachedInputTokens,
+			}
+		}
+		out["usage"] = usageMap
 	}
 	return out
 }
@@ -877,7 +883,42 @@ func usageFromOpenAI(result map[string]any) Usage {
 	if total == 0 {
 		total = input + output
 	}
-	return Usage{InputTokens: input, OutputTokens: output, TotalTokens: total}
+	cachedInput := cachedInputTokensFromOpenAIUsage(usage)
+	if cachedInput > input && input > 0 {
+		cachedInput = input
+	}
+	return Usage{InputTokens: input, OutputTokens: output, CachedInputTokens: cachedInput, TotalTokens: total}
+}
+
+func cachedInputTokensFromOpenAIUsage(usage map[string]any) int {
+	if len(usage) == 0 {
+		return 0
+	}
+	promptDetails, _ := firstPresent(usage["prompt_tokens_details"], usage["promptTokensDetails"]).(map[string]any)
+	inputDetails, _ := firstPresent(usage["input_tokens_details"], usage["inputTokensDetails"]).(map[string]any)
+	usageMetadata, _ := usage["usageMetadata"].(map[string]any)
+	return intFromAny(firstPresent(
+		promptDetails["cached_tokens"],
+		promptDetails["cachedTokens"],
+		promptDetails["cache_read_input_tokens"],
+		promptDetails["cacheReadInputTokens"],
+		inputDetails["cached_tokens"],
+		inputDetails["cachedTokens"],
+		inputDetails["cache_read_input_tokens"],
+		inputDetails["cacheReadInputTokens"],
+		usage["prompt_cache_hit_tokens"],
+		usage["promptCacheHitTokens"],
+		usage["cached_tokens"],
+		usage["cachedTokens"],
+		usage["cached_input_tokens"],
+		usage["cachedInputTokens"],
+		usage["cache_read_input_tokens"],
+		usage["cacheReadInputTokens"],
+		usage["cached_content_token_count"],
+		usage["cachedContentTokenCount"],
+		usageMetadata["cached_content_token_count"],
+		usageMetadata["cachedContentTokenCount"],
+	))
 }
 
 func requestIDFromHTTPResponse(resp *http.Response) string {