Hi, a few notes. First, rstanarm (and brms, bambi, etc) do a lot of convenient transformations/rescaling automatically to improve sampling efficiency that you will need to do yourself if you write the model in Turing (or Stan, etc).
I highly recommend reading Prior Distributions for rstanarm Models • rstanarm. Importantly, none of these parameters have flat default priors. They give the default (unscaled) prior for ϵ (prior_aux) as Exponential(1) and the default (unscaled, after centering) prior for a as Normal(20, 2.5). Also, rstanarm internally centers the predictors (subtracts their mean). I’m not certain if it also divides them by their standard deviation, but it at least uses the standard deviation to rescale the priors.
In case you’re not aware, there’s also TuringGLM, which aims to be the brms of Turing.