### Tested versions

v4.2.stable.official [46dc27791]

### System information

Windows 11- Godot v4.2.stable.official [46dc27791] - Vulkan (Forward+)

### Issue description

When I switch picker mode the next time I open it should be the pick mode I selected last time but it's not

https://github.com/godotengine/godot/assets/46812028/522c8b55-14cf-4781-963f-a465a03c9432



### Steps to reproduce

Toggle a picker mode off and on again

### Minimal reproduction project (MRP)

N/A
ERR_FAIL_NULL_V_MSG(p_object, nullptr, "Object cannot be null.");
	Ref<Script> scr = p_object->get_script();
	if (scr.is_null() && p_object->is_class("Script")) {
		scr = p_object;
	}
	return _get_class_or_script_icon(p_object->get_class(), scr, p_fallback);
}
Ref<Texture2D> EditorNode::get_class_icon(const String &p_class, const String &p_fallback) {
	ERR_FAIL_COND_V_MSG(p_class.is_empty(), nullptr, "Class name cannot be empty.");
	Ref<Script> scr;
	if (ScriptServer::is_global_class(p_class)) {
		scr = EditorNode::get_editor_data().script_class_load_script(p_class);
	}
	return _get_class_or_script_icon(p_class, scr, p_fallback, true);
}
bool EditorNode::is_object_of_custom_type(const Object *p_object, const StringName &p_class) {