It doesn’t really. Obviously the alleged security breach is egregious and if they’re committing crimes they should be prosecuted. But given that they’re relatively young, part of me wonders if these guys are being exploited by Musk and Thiel and will be scapegoated if the political winds start blowing another way. But that makes no difference to their criminal liability.
Some of the key actions taken or threatened by DOGE are at least arguably illegal without permission from Congress, such as dismantling USAID, offering "deferred resignation" firing employees without due process, unilaterally stopping payments to agencies or individuals, and some smaller ones. Beyond that, there is the FACA lawsuit challenging the organization of DOGE itself; the administration has partially mitigated that by making Musk a special government employee, but no word on the rest of DOGE.