If you had more than two groups, you could do what is called a meta-analysis.  That is where you take the observed effects across different populations and pool them to get a population effect (I'm being very fast and loose here).

Because you have two experiments, there is no good justification for doing a meta analysis and so I think your best bet is to simply fit a mixed model (be it Bayesian or otherwise).  Here is a small example:

In the two populations, say I made 100 and 120 clicks on 6000 and 5500 impressions respectively. This results in a 1.7% and 2.2% click through ratio.  These estimates are variable because they come from different populations.  The goal is to estimate the click through ratio for the ad marginalized over populations.

Here is the code to do so:

    library(tidyverse)
    library(rstanarm)
    library(lme4)
    
    inv.logit = function(x) 1/(1+exp(-x))
    
    d = tribble(
      ~'click', ~'impression', ~'population',
      100, 6000, 'A',
      120, 5500, 'B'
    )
    
    model = glmer(cbind(click, impression-click) ~ 1 + (1|population),
                       data = d,
                       family = binomial())
    
    model %>% summary


The coefficient for the intercept of this model is our estimate for the click through rate (on the log odds scale).  To get the probability, we can do `inv.logit(fixef(model))` which returns a probability of 1.9%.

An even easier way would be to do a weighted average of the CTR.  Weight the CTR by their variance and then average them.  

    d$p = d$click/d$impression
    
    d$var = d$p*(1-d$p)
    
    d$w = d$var/sum(d$var)
    
    est = d$p %*% d$w
    
    est

Similar number, no confidence intervals this way (at least, not easily).

As an aside, I don't think doing this is a great idea.  If users are distinct between regions, then including more regions into this analysis will yield a better estimate of the population level CTR.  Its obviously your decision, but this doesn't sound robust to me.