It's a wee bit more complicated:

• Executive orders created the DOGE service out of USDS, but also a separate "DOGE Temporary organization".
• it's not clear how the temporary organization is distinct from the old USDS, or if it even exists in fact (i.e. has it been staffed up at all?)
• The government seems to argue that many of the identified DOGE Team personnel are actually employed by the individual agencies they embed in under various titles and SGE authorizations.
• So if the DOGE Team members are not in the DOGE Service, and not in the temporary organization, how does the command and control work?
• Elon Musk is allegedly not affiliated with either of the DOGE organizations. He may or may not be a special government employee in a generic White House sub-office. He definitely, allegedly, doesn't have any decision making authority. (But then, how come he talks about making a bunch of decisions on Xitter?)