The Add-ons view is not very helpful.
It would be nice to get a detailed view with more information about the state and version and so on.
You can technically see it in the addons overview because the icon is grayed out. For example in the picture the phpMyAdmin addon is not running, File editor is. However this is not a very clear indicator expecially if the icon is already gray-ish by itself. An icon would probably be clearer.
FYI addons also have entities that indicate if they are running or not. You can find them in the “Home Assistant Supervisor” integration. There is an entry for every addon where you can enable the entities you are interested in so that way you could put them on a dashboard somewhere.
The Running entity indicates if it is running. In this case it is “Niet actief” which means “Not active”, the CPU/Memory are not available because it is not running.
The add-ons view is horrendous. Even the ability to separate running from not running would be a huge upgrade!