The elemwise log-likelihood is not stored in the InferenceData that nutpie returns, even when asking for it. The following for instance doesn't error out, but doesn't add a log_likelihood group to the trace (whereas it does when using the default PyMC sampler):

y = np.array([28, 8, -3, 7, -1, 1, 18, 12])
sigma = np.array([15, 10, 16, 11, 9, 11, 10, 18])
J = len(y)

with pm.Model() as pooled:
    mu = pm.Normal("mu", 0, sigma=10)
    obs = pm.Normal("obs", mu, sigma=sigma, observed=y)

    trace_p = pm.sample(nuts_sampler="nutpie", idata_kwargs={"log_likelihood": True}) # doesn't store
    trace_p_ = pm.sample(idata_kwargs={"log_likelihood": True}) # does store

In PyMC it's not that big of a deal (although it adds friction to the user workflow), as one can just do:

with pooled:
    pm.compute_log_likelihood(trace_p)

But that may be a small issue for Bambi users, which are usually less advanced (cc @tomicapretto). They'd have to do pooled.compute_log_likelihood(trace_p), which takes much more time to compute