I think that the core issue here is conflict (specifically, a timing conflict) between the state law utilized by Youngkin and a related federal statute that proscribes a different timeline.
I can't say I've taken much time in getting super familiar with the details. But, if that's the case, then I don't think this is a case of the DOJ just brazenly trying to make it possible for non-citizens to vote. And it's being cast that way.
Personally, I think what a state should do in a situation like (although VA's law may not allow for this) is to just accept provisional ballots from anybody in question. That gives the state more time to properly vet them and determine if they are or aren't eligible. If they're eligible, count it and take steps to ensure they aren't back on a list subject to being culled from the registry...if they aren't, toss it and then get them off the rolls.