fix(gemini): preserve google search in Claude compat tools

backend/internal/service/gemini_messages_compat_service_test.go

@@ -164,6 +164,35 @@ func TestConvertClaudeToolsToGeminiTools_CustomType(t *testing.T) {
 	}
 }
 
+func TestConvertClaudeToolsToGeminiTools_PreservesWebSearchAlongsideFunctions(t *testing.T) {
+	tools := []any{
+		map[string]any{
+			"name":         "get_weather",
+			"description":  "Get weather info",
+			"input_schema": map[string]any{"type": "object"},
+		},
+		map[string]any{
+			"type": "web_search_20250305",
+			"name": "web_search",
+		},
+	}
+
+	result := convertClaudeToolsToGeminiTools(tools)
+	require.Len(t, result, 2)
+
+	functionDecl, ok := result[0].(map[string]any)
+	require.True(t, ok)
+	funcDecls, ok := functionDecl["functionDeclarations"].([]any)
+	require.True(t, ok)
+	require.Len(t, funcDecls, 1)
+
+	searchDecl, ok := result[1].(map[string]any)
+	require.True(t, ok)
+	googleSearch, ok := searchDecl["googleSearch"].(map[string]any)
+	require.True(t, ok)
+	require.Empty(t, googleSearch)
+}
+
 func TestGeminiHandleNativeNonStreamingResponse_DebugDisabledDoesNotEmitHeaderLogs(t *testing.T) {
 	gin.SetMode(gin.TestMode)
 	logSink, restore := captureStructuredLog(t)