Should Twitter itself get a state sponsored label for getting concessions from San Francisco on their headquarters? https://www.sfgate.com/bayarea/article/S-F-controller-hails-... Should Elon's account (or SpaceX or Telsa) have the same label because of their significant government funding? It's hard to see this as anything but silly politics games.
"media"
EDIT: lots of discussion around this. Twitter is literally a social media company. You can split hairs on whether the “media” part of “social media” agrees with your bias here.