Ok, I think I got it. For the second question (the first, I am 90% confident it’s ok), would be something like:
with my_model:
# To find difference of the posteriors we find the mean of each
# num_chains*num_samples_per_chain and then subtract them
mean_1st_weeks = np.mean(pred["first_weeks"], axis=1)
print(mean_1st_weeks.shape)
mean_2nd_weeks = np.mean(pred["second_weeks"], axis=1)
print(mean_2nd_weeks.shape)
# Now:
diff = mean_1st_weeks - mean_2nd_weeks
print(diff.shape)
print(diff)
az.plot_posterior(diff, ref_val=0)

With an increase of the 94% HDI width, as one would expect from a posterior sample. Now I think this second question is ok with 90% of confidence, too.