I think Switzerland (could be some neighboring country) is piloting a CBDC that is just issued atop Ethereum. In principle it may not need to be different, regulation wise, from a privately issued stablecoin. If we're talking asset-backed stablecoins, it seems the idea so far is to regulate the issuers as "insured depository institutions" and just enforce certain requirements regarding the reserves, to protect this notion of one-to-one exchangeability between dollars and stablecoins.
That's all to say, a CBDC needn't necessarily involve some panopticon, public or private. I did a moderately through report for stablecoins for Humanity Forward, but it didn't touch on CBDCs per se.
Not sure about Switzerland though, so don't quote me haha.