Invisible = Sign-in but do not broadcast the games you are playing (though your profile will show that you signed-in)
Offline = Stay offline and do not sign-inOn the profile of a friend you can see the last time they signed-in to their account:
https://preview.redd.it/can-anyone-beat-my-last-online-frien...
Before it was public, and now restricted (for a couple of years already) to friends only.
I guess this is why they won't change it, since it's a feature.
Because from the fields in the protobuf I somewhat suspect it's the same, but I get your point of view as well
EDIT: If it's not, then my bad
I got one from work that I don't use much outside of travel and haven't changed in any way past initial setup. It stays connected to WiFi and continuously broadcasts various discovery packets for the past month and a half since I last opened it up.