This is because of a recent SCOTUS decision that held a state can only us U.S. citizenship as a requirement for voting in state elections, but can't enforce it for elections to Federal offices. However, this also creates an easy way for the Federal government to check on whether a person voting in a Federal election is a U.S. citizen, as required by Federal law. All it needs to do is get the AZ "Federal qualified only" list and require each person on thatlist to prove his/her citizenship to ICE.
Requires federal law changes to implement so not a short term solution. A better solution that only requires changes at the (GOP controlled) AZ. Cross reference the AZ 'federal only' voter registration list and the publicly available lists of who's voted to produce the list of 'federal only' voted. In their normal course of business AZ will periodically definitively identify individuals as "non-citizens." Mandate all such identifications be cross-referenced with the state held list of 'federal only' voted. Mandated that all matches be forwarded to the US Attorney for illegal voting. People can still vote on the federal honor system, but if they're dishonorable and get caught anyway by the state as a non-citizen they don't get away with it. And the US attorney can then check whether any of their non-citizen family is on the list. You at least partially disincentivise the process.