> You are correct. The property that the colluding website and DMV still cannot identify you is called "unlinkability" and as far as I can tell cannot be achieved without zero-knowledge proofs.
Well, no. This is true only if you trust the unverifiable wallet software on your phone, which was provided by a for-profit, American big tech advertising company. In this protocol, the wallet may secretly leak the transaction details back to the DMV or whoever else they wish[1].
[1] "Yes, a malicious wallet could leak your information." >>44458549
Your observation that a bad wallet could compromise unlinkability is not a refutation of that. To refute it you need to show that it is possible to achieve unlinkability without using a ZKP.