### 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(p_editing_owner);
	
	if (!p_object || _is_class_editor_disabled_by_feature_profile(p_object->get_class())) {
		
		hide_unused_editors(p_editing_owner);
		return;
	}
	
	Vector<EditorPlugin *> available_plugins = editor_data.get_handling_sub_editors(p_object);
	if (available_plugins.is_empty()) {
		
		hide_unused_editors(p_editing_owner);
		return;
	}
	ObjectID owner_id = p_editing_owner->get_instance_id();
	
	
	List<EditorPlugin *> to_remove;
	for (EditorPlugin *plugin : active_plugins[owner_id]) {
		if (!available_plugins.has(plugin)) {
			to_remove.push_back(plugin);
			if (plugin->can_auto_hide()) {
				_plugin_over_edit(plugin, nullptr);
			} else {
				
				_plugin_over_self_own(plugin);
			}
		}