i was reading a bayes re-analysis yesterday that did this, it might not be the best example tho: bayes re-analysis, ECMO RCT. They say:
“data-derived prior distributions were developed based on relevant studies18-20 from a meta-analysis of ECMO for ARDS.21 The treatment effects in these previous studies were combined with the observed data from this trial in a Bayesian hierarchical random-effects model (that itself used minimally informative priors)”
they make too much of the convention of having artificial priors that are on the spectrum: enthusiastic - sceptical (shown in table 1). But i thinks this gets at the point you mention ie