fix(antigravity): strip billing header from system instruction before upstream call

The x-anthropic-billing-header block in the Claude system array is
client-internal metadata and should not be forwarded to the Gemini
upstream as part of systemInstruction.parts.

internal/translator/antigravity/claude/antigravity_claude_request.go

@@ -101,6 +101,9 @@ func ConvertClaudeRequestToAntigravity(modelName string, inputRawJSON []byte, _
 			systemTypePromptResult := systemPromptResult.Get("type")
 			if systemTypePromptResult.Type == gjson.String && systemTypePromptResult.String() == "text" {
 				systemPrompt := systemPromptResult.Get("text").String()
+				if strings.HasPrefix(systemPrompt, "x-anthropic-billing-header:") {
+					continue
+				}
 				partJSON := []byte(`{}`)
 				if systemPrompt != "" {
 					partJSON, _ = sjson.SetBytes(partJSON, "text", systemPrompt)