I wrote up a poor man’s version of this type of prior for a beta and binomial combination on this forum.
The key part is the prior on the centered and scaled predictors on the logit scale.
It’s nothing fancy but by doing that the total sd from the predictors (sd(X\gamma)) gets a prior of \sigma_{\gamma} which you can set according to what is appropriate (or maybe even give it its own prior). I am not sure how to directly related it to ROC AUC.
I thought of the \sigma_y as an indicator of how sure you expect the model to be if the predictors strongly point to one of two outcomes for an observation. Maybe that observation is 3 \sigma_{\gamma} away from the mean on the logit scale. If \sigma_{\gamma} = 1, this implies a probability of inv\_logit(3) = 0.95. If \sigma_y = 2, this implies a probability of inv\_logit(6) = 0.997. Or you could think about how well you think the model will discriminate between an observation that is \sigma_{\gamma} away and an observation that is -\sigma_{\gamma} away.