I would agree with @torkar that plotting is one solution to this.
The crux of the non identity links is that stuff ceises to be linear, which leads to the problem you describe here:
The conclusion of that observation is, that coefficients (and their priors) in a model with a log/logit link (or any non-identity link that looses linearity) can only be understood in the context of the entire model.
I remember having a similar question but apparently I never asked it here myself. But I remember reading an answer to that question that was a from a book and stated the same thing.
When I worked on an analysis with a similar problem I had prior values for the mean of the data but not the effect sizes, so what I did was transform the mean values to the logit scale and then, starting from the default priors, iterate over the other priors until the pp_check plot matches my prior knowledge.
Ultimately, my intuition is on the outcome scale. I know that it is unreasonable for the outcome to be bigger then eg. 100. So I tune the priors until the pp_check shows a curve that matches this expectation.
An even better way seems to be the new adjustr package, though I haven’t tried this one myself: adjustr: Stan Model Adjustments and Sensitivity Analyses using Importance Sampling • adjustr