### 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
ObjectID current_id = editor_history.get_current();
	Object *current_obj = current_id.is_valid() ? ObjectDB::get_instance(current_id) : nullptr;
	Ref<Resource> res = Object::cast_to<Resource>(current_obj);
	if (p_skip_foreign && res.is_valid()) {
		const int current_tab = scene_tabs->get_current_tab();
		if (res->get_path().find("::") > -1 && res->get_path().get_slice("::", 0) != editor_data.get_scene_path(current_tab)) {
			
			current_obj = nullptr;
		}
	}
	bool inspector_only = editor_history.is_current_inspector_only();
	this->current = current_obj;
	if (!current_obj) {
		SceneTreeDock::get_singleton()->set_selected(nullptr);
		InspectorDock::get_inspector_singleton()->edit(nullptr);
		NodeDock::get_singleton()->set_node(nullptr);
		InspectorDock::get_singleton()->update(nullptr);
		hide_unused_editors();
		return;
	}
	
	bool disable_folding = bool(EDITOR_GET("interface/inspector/disable_folding")) || current_obj->is_class("EditorDebuggerRemoteObject");
	if (InspectorDock::get_inspector_singleton()->is_using_folding() == disable_folding) {
		InspectorDock::get_inspector_singleton()->set_use_folding(!disable_folding, false);
	}
	bool is_resource = current_obj->is_class("Resource");