From the error it looks like an issue with the dtypes of the data, or probably not even of the data but the coordinates that index the data. Can you share what you get when you run
print(tr.log_likelihood)
for the case that fails? That should include the shapes and dtypes of the different elements and even if not the whole trace to reproduce the error it might already be enough.
I am not expert on pickle, but it is always a source of headaches, I strongly recommend you use to_netcdf or to_zarr: InferenceData — ArviZ dev documentation