I think you should add an attribute which defines some specific traits of your process or netwerk entities, as for now you cannot use checkboxes because your only available attributes on these entities are strings.
Furthermore I think you can accomplish the above described scenario with some on-change microflows; whenever you select a option on the left side, a microflow can be triggered which retrieves a list of Pakket objects based on the selection you made with your checkboxes.
alternatively you could opt to make a selection in your left-bar and also add a button in this bar with a caption like 'filter' or 'refresh'. You can then execute the retrieve MF from here.
Also, if I understand your question correctly, you are wondering how to display the list correctly in a list view? If so, you can do so by setting an association between the Pakket objects which should be displayed and a parent object (can even be currentUser). When de-selecting an filter option, you just empty the association again.