Below configuration adding isEmpty operator for REFERENCE type and in operator for ENUM.
<bean id="editorConditionConfiguration" parent="myCockpitEditorConditionConfiguration" scope="tenant"/>
<bean id="myCockpitEditorConditionConfiguration" parent="defaultEditorConditionConfiguration" scope="tenant"
class="de.hybris.platform.cockpit.model.advancedsearch.config.impl.DefaultEditorConditionConfiguration" abstract="true">
<property name="defaultConditionsMap">
<map merge="true">
<entry key="REFERENCE" value="isEmpty"/>
<entry key="ENUM" value="in"/>
</map>
</property>
</bean>
<bean class="de.hybris.platform.cockpit.services.search.impl.ConditionTranslatorRegistry.ConditionTranslatorMapping">
<property name="attributeTypes">
<set>
<value>REFERENCE</value>
</set>
</property>
<property name="operatorQualifiers">
<set>
<value>isEmpty</value>
</set>
</property>
<property name="translator" ref="genericQueryConditionTranslator"/>
</bean>
<bean class="de.hybris.platform.cockpit.services.search.impl.ConditionTranslatorRegistry.ConditionTranslatorMapping">
<property name="attributeTypes">
<set>
<value>ENUM</value>
</set>
</property>
<property name="operatorQualifiers">
<set>
<value>in</value>
</set>
</property>
<property name="translator" ref="genericQueryConditionTranslator"/>
</bean>
You need to add this operator to your referenced property with below code in your advanced search configuration (advancedSearch_VariantProduct.xml).
<property qualifier="product.galleryImages" visible="false">
<conditions mode="append">
<condition operator="isEmpty"></condition>
</conditions>
</property>