My suggestion is to separate the person and iid observations into separate axis like this:
"n": np.random.poisson(lam = 15, size = (74, 3)), "person_id": np.repeat([[0,1,2]], (74, 1))
and finally set the shape of the observations RV to shape=n_persons. The idea behind this is that you want to have the model specified well in the absence of observed data. By specified well I mean that sample_prior_predictive should work and its output for the observations RV should have the same shape as your fake data, when you ask to get 74 samples.