In tasks with Geometry collection, objects will be automatically grouped in the right-side menu. They do not differ from other objects in any other way.
You're able to switch into a object group if you have a group selected by using the Alt+Tab shortcut. This will select the first object in the group without using your mouse.
The functioanlity is now in place so that you're able to jump between the different objects within the group using your regular Tab and Shift+Tab Shortcuts.
If an object has been created in the wrong collection and you wish to move it - you will use the 'cut' and 'paste' functionallity. Right-click on an object inside of a collection and select 'Cut'. Then you can select another collection and paste the object, either by right clicking in the object list or with ctrl+v.
The cut operation has no default shortcut. However, you can bind it to a custom shortcut if you are using it frequently.