fix(gemini): support includeServerSideToolInvocations in GeminiToolConfig

- Add IncludeServerSideToolInvocations field to GeminiToolConfig to prevent dropping client tool settings.
- Fix HTTP 400 error when mixing built-in tools (e.g. Google Search) with function calling on Gemini 3.6/3.7 models.
- Add serialization/deserialization unit test TestGeminiToolConfig_IncludeServerSideToolInvocations.

Fixes #5709

backend/internal/pkg/antigravity/gemini_types.go

@@ -112,7 +112,8 @@ type GeminiImageSearch struct {
 
 // GeminiToolConfig Gemini 工具配置
 type GeminiToolConfig struct {
-	FunctionCallingConfig *GeminiFunctionCallingConfig `json:"functionCallingConfig,omitempty"`
+	FunctionCallingConfig            *GeminiFunctionCallingConfig `json:"functionCallingConfig,omitempty"`
+	IncludeServerSideToolInvocations *bool                        `json:"includeServerSideToolInvocations,omitempty"`
 }
 
 // GeminiFunctionCallingConfig 函数调用配置

backend/internal/pkg/antigravity/request_transformer_test.go

@@ -565,3 +565,27 @@ func TestTransformClaudeToGeminiWithOptions_PreservesWebSearchAlongsideFunctions
 	require.Equal(t, "get_weather", req.Request.Tools[0].FunctionDeclarations[0].Name)
 	require.NotNil(t, req.Request.Tools[1].GoogleSearch)
 }
+
+func TestGeminiToolConfig_IncludeServerSideToolInvocations(t *testing.T) {
+	t.Run("serialize and deserialize toolConfig with includeServerSideToolInvocations", func(t *testing.T) {
+		trueVal := true
+		cfg := GeminiToolConfig{
+			FunctionCallingConfig: &GeminiFunctionCallingConfig{
+				Mode: "VALIDATED",
+			},
+			IncludeServerSideToolInvocations: &trueVal,
+		}
+
+		data, err := json.Marshal(cfg)
+		require.NoError(t, err)
+		require.Contains(t, string(data), `"includeServerSideToolInvocations":true`)
+
+		var decoded GeminiToolConfig
+		err = json.Unmarshal(data, &decoded)
+		require.NoError(t, err)
+		require.NotNil(t, decoded.IncludeServerSideToolInvocations)
+		require.True(t, *decoded.IncludeServerSideToolInvocations)
+		require.Equal(t, "VALIDATED", decoded.FunctionCallingConfig.Mode)
+	})
+}
+